phd stavros tsantis

We thank the Operational Program for Educational and Vocational Training II (EPEAEK II) for funding this PhD thesis.

UNIVERSITY OF PATRAS

SCHOOL OF HEALTH SCIENCES SCHOOL OF NATURAL SCIENCES

FACULTY OF MEDICINE DEPARTMENT OF PHYSICS

INTERDEPARTMENTAL POSTGRADUATE PROGRAM IN

MEDICAL PHYSICS

PhD Thesis

Image Processing and Analysis Methods in Thyroid Ultrasound Imaging

Tsantis Stavros

Patras, 2007, Hellas

Ευχαριστούμε το Επιχειρησιακό Πρόγραμμα Εκπαίδευσης και Αρχικής Επαγγελματικής Κατάρτισης (ΕΠΕΑΕΚ ΙΙ) για την χρηματοδότηση της διδακτορικής διατριβής

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ

ΤΜΗΜΑ ΙΑΤΡΙΚΗΣ ΤΜΗΜΑ ΦΥΣΙΚΗΣ

ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ

ΙΑΤΡΙΚΗ ΦΥΣΙΚΗ

Διδακτορική Διατριβή

Μέθοδοι Επεξεργασίας και Ανάλυσης Υπερηχογραφικής Εικόνας του Θυρεοειδούς Αδένα

Σταύρος Τσαντής

Πάτρα, 2007

SUPERVISING COMMITTEE

1. George Nikiforidis, Professor, Department of Medical Physics, University of Patras

(Supervisor), Greece

2. Dionisis Cavouras, Professor, Department of Medical Instruments Technology,

Technological Institute of Athens, Greece

3. Vassilis Anastasopoulos, Professor, Department of Physics, University of Patras,

Greece

EXAMINING COMMITTEE

1. George Nikiforidis, Professor, Department of Medical Physics, University of Patras,

Greece.

2. Vassilis Anastasopoulos, Professor, Department of Physics, University of Patras,

Greece.

3. George Panayiotakis, Professor, Department of Medical Physics, University of

Patras, Greece.

4. Anastasios Bezerianos, Professor, Department of Physics, University of Patras,

Greece.

5. Dimitrios Siamplis, Professor, School of Medicine, University of Patras, Greece.

6. Kostas Berberidis, Associate Professor, Department of Computer Engineering and

Informatics, University of Patras, Greece.

7. George Oikonomou, Assistance Professor, Department of Physics, University of

Patras, Greece.

Η έμπνευση διαψεύδει την αντίληψη

Σοφοκλής (496 – 406 π.Χ)

Inspiration denies perception

Sofoklis (496 – 406 b.C)

ACKNOWLEDGEMENTS

I wish to express my gratitude to my supervisor Professor G. Nikiforidis for the

assignment of this project and for his suggestions and guidance throughout this thesis.

I am also grateful to Professor D. Cavouras for his faith and confidence towards me and

for his contribution in the fulfillment of this thesis. I would also like to thank him for his

valuable guidelines in writing scientific articles.

I would like to thank Dr N. Dimitropoulos for his selfness support throughout this thesis,

his proposition regarding the topic of this thesis and his valuable medical guidelines

regarding thyroid imaging.

I would also like to thank N. Arikidis mainly for his friendship and for the long

conversations regarding wavelet theory, Dr I. Kalantzis and Dr N. Piliouras for their

important guidance in pattern recognition theory and algorithms.

Finally, I wish to express my gratitude to my parents for their constant support and

encouragement during the years of that work.

TABLE OF CONTENTS

ΕΛΛΗΝΙΚΗ ΠΕΡΙΛΗΨΗ-SUMMARY IN GREEK

CHAPTER 1 – Introduction 1

1.1 Power of Ultrasound 11.2 Need for Image Processing and Analysis Methods in Thyroid Ultrasound Images 11.3 Aims and Novelties of Thesis 2

1.3.1 Wavelet–Based Image Processing 21.3.2 Image Analysis 4

1.4 Publications 51.5 Dissertation Layout 7

CHAPTER 2 – Thyroid Gland 9

2.1 Introduction 92.2 Thyroid Disorders 102.3 Management of Solitary Nodules 112.4 Grading 13

CHAPTER 3 – Physics & Instrumentation of Ultrasound 15

3.1 Nature of Ultrasound 153.2 Propagation in Tissue 153.3 Pulse – Echo Imaging 163.4 Instrumentation 163.5 Quality control of the ultrasound system 173.6 Data Acquisition and Storage 18

CHAPTER 4 – The Wavelet Transform 21

– Summary 214.1 Wavelet Theory 214.2 Continuous Wavelet transform 224.3 Redudant Dyadic Wavelet Transform (1-D) 234.4 Redudant Dyadic Wavelet Transform (2-D) 284.5 Multiscale edge representation 32

CHAPTER 5 – Singularity Detection 35

– Summary 355.1 Singularity and mathematical description 355.2 Wavelet transform and singularity 365.3 Singularity Detection (1-D) 385.4 Singularity Detection (2-D) 41

CHAPTER 6 – Pattern Recognition 43

– Summary 436.1 Pattern Recognition Theory 436.2 Object Isolation 446.3 Feature Generation 446.4 Textural Features 44

6.4.1 First order statistical features 446.4.2 Second order statistical features 45

6.4.2.1 Co-Occurrence matrix features 456.4.2.2 Run-Length matrix features 48

6.4.3 Shape and Geometrical features 50 6.4.4 Local maxima features 536.5 Data Normalization 536.6 Classification task 54

6.6.1 Minimum distance classifiers 546.6.2 Bayesian classifier 556.6.3 Neural networks classifiers 556.6.4 The Support Vector Machines Classifier 57

CHAPTER 7 – Wavelet-based speckle suppression in ultrasound images 61

– Summary 617.1 Review of the Literature 617.2 Materials and methods 64

7.2.1 Overview and Implementation of the Algorithm 647.2.2 Speckle Model 657.2.3 Inter-scale Wavelet Analysis 67

7.2.3.1 Dyadic Wavelet Transform 677.2.3.2 Gradient Vector 697.2.3.3 Modulus Maxima 697.2.3.4 Lipschitz Regularity 717.2.3.5 Detection of singularities 71

7.3 Experimental Results and Evaluation 757.3.1 Tissue mimicking Phantom Validation 767.3.2 US image Case Study 767.3.3 Observer evaluation study 81

7.4 Discussion and Conclusions 85

CHAPTER 8 - Thyroid Nodule Boundary Detection in ultrasound images 87

– Summary 878.1 Review of the Literature 878.2 Materials and Methods 92

8.2.1. Overview and implementation of the algorithm 928.2.2. US data Acquisition 948.2.3. Edge Detection Procedure 94

8.2.3.1. Multiscale Edge Representation 948.2.3.2. Coarse to Fine Analysis 95

8.2.4. Multi-scale Structure Model 968.2.4.1. Maxima Linking 978.2.4.2. Structure Identification 98

8.2.5. Nodule’s Boundary Extraction 998.3.1. Constrained Hough Transform 1008.3.2. Accumulator Local Maxima Detection 100

8.3 Results 1018.4 Discussion and Conclusion 106

CHAPTER 9 – Development of a Support Vector Machine – Based Image Analysis System for Assessing the Thyroid Nodule Malignancy Risk on Ultrasound 109

– Summary 109 9.1 Review of the Literature 1099.2 Materials and Methods 110

9.2.1 US image data acquisition 1109.2.2 Data pre-processing 1119.2.3 Classification 1119.2.4 Support vector machine classifier 1129.2.5 Multilayer perceptron (MLP) classifier 1139.2.6 Quadratic least squares minimum distance classifier 1139.2.7 Quadratic Bayesian classifier 1139.2.8 Support Vector Machines Wavelet Kernels 114

9.2.8.1 Wavelet Kernels implementation 1149.2.9 System performance evaluation 116

9.3 Results and discussion 1169.3.1 SVM Classification Outcome 1169.3.2 MLP Classification Outcome 1199.3.3 GLSMD & QB Classification Outcome 1209.3.4 SVM with Wavelet Kernels Classification Outcome 122

CHAPTER 10 – Pattern Recognition Methods Employing Morphological and Wavelet Local Maxima Features towards Evaluation of Thyroid Nodules Malignancy Risk in Ultrasonography 127

– Summary 127 10.1 Materials and Methods 127

10.1.1 Patients 12710.1.2 Feature extraction 12810.1.3 Feature selection and classification 129

10.2 Results and discussion 13010.2.1 SVM & PNN model Evaluation without the presence of Speckle 13010.2.2 SVM & PNN model Evaluation with the presence of Speckle 136

10.3 Conclusion 139

CHAPTER 11 – Conclusion and Future Work 141

11.1 Conclusion 141 11.2 Feature Work 142

REFERENCES 143

APPENDIX I List of Figures 157

APPENDIX II List of Tables 161

APPENDIX III Abbreviations 163

APPENDIX III Index of Terms 165

I

ΜΕΘΟΔΟΙ ΕΠΕΞΕΡΓΑΣΙΑΣ ΚΑΙ

ΑΝΑΛΥΣΗΣ ΥΠΕΡΗΧΟΓΡΑΦΙΚΗΣ

ΕΙΚΟΝΑΣ ΤΟΥ ΘΥΡΕΟΕΙΔΟΥΣ

ΑΔΕΝΑ

Εισαγωγή

Η καθιέρωση της υπερηχογραφίας ως ένα πολύτιμο εργαλείο στην πλειονότητα των ιατρικών

εφαρμογών παγκοσμίως, συνδέεται άμεσα με την ραγδαία τεχνολογική εξέλιξη των συστημάτων

απεικόνισης που υιοθετούνται στην ιατρική και τη βιολογία. Ο σχεδιασμός και η υλοποίηση

ολοένα και πιο σύγχρονων συστημάτων απεικόνισης έδωσε την δυνατότητα στην υπερηχογραφία

να διεισδύσει σε ιατρικές ειδικότητες, όπως η Ορθοπεδική, η Εντατική θεραπεία, η Διαβητολογία

κλπ., στις οποίες λίγα έτη πριν, η εφαρμογή της ήταν απαγορευμένη. Το γεγονός αυτό μετέβαλε

ριζικά την φύση της προληπτικής ιατρικής στην σύγχρονη εποχή. Στην πραγματικότητα, η

υπερηχογραφική εξέταση αναγνωρίζεται πλέον ως μια θεμελιώδης τεχνική στην πρόληψη, τη

διάγνωση και τη θεραπεία ενός συνεχώς διευρυνόμενου φάσματος ασθενειών. Η υπερηχογραφία

επέτυχε να επιβάλει την παρουσία της σε κάθε ιατρό. Από μια μικρή ιδιωτική κλινική μέσω μιας

φορητής μονάδος, ως ένα γενικό νοσοκομείο μέσω ενός ακριβού συστήματος απεικόνισης

τεσσάρων διαστάσεων, ο υπέρηχος αποδεικνύει την αποτελεσματικότητα και την ακρίβειά του σε

καθημερινή βάση.

Η ψηφιακή απεικόνιση του θυρεοειδούς αδένα, τόσο μέσω της κλασσικής δισδιάστατης B-Mode

εικόνας όσο και μέσω της έγχρωμης απεικόνισης Doppler, καθιστά την υπερηχογραφία ένα

αξιόπιστο και εύχρηστο μέσο για την κλινική αξιολόγηση του. Η υψηλή διακριτική ικανότητα

των σύγχρονων αυτών συστημάτων παρέχει στον Ιατρό την δυνατότητα να εντοπίσει την ύπαρξη

όζων – είτε συμπαγών είτε κολλοειδών – στον θυρεοειδή αδένα ακόμα και με διαστάσεις πολύ

μικρές (1mm) [14-28]. Επίσης, η υπερηχογραφική εικόνα επιτρέπει την λήψη βιοψίας (Fine

Needle Aspiration - FNAΒ) σε πραγματικό χρόνο για την περαιτέρω αξιολόγηση του όζου [29-

33]. H διεθνής αρθογραφία αμφισβήτησε την προηγούμενη δεκαετία την υπερηχογραφική

εικόνα, ως ένα αξιόπιστο μέσο για τον διαχωρισμό ενός κακοήθους από έναν καλοήθη όζο. Στην

II

κλινική διάγνωση ωστόσο, πληθώρα υπερηχογραφικών χαρακτηριστικών όπως η ηχογένεια, το

περίγραμμα, η παρουσία αποτιτανώσεων και η διόγκωση με τον χρόνο έχουν καθιερωθεί τα

τελευταία χρόνια ως ενδείξεις πιθανής κακοήθειας [185-190]. Αυτό το γεγονός, σε συνδυασμό με

την έλλειψη πρόσφατων ποσοτικών μελετών στην αξιολόγηση της φύσης των όζων, καθιστά

απαραίτητη την έρευνα για τον σχεδιασμό και υλοποίηση αλγορίθμων επεξεργασίας και

αναγνώρισης προτύπων στην υπερηχογραφική εικόνα. Οι αλγόριθμοι αυτοί έχουν ως σκοπό την

αύξηση της ακρίβειας ταξινόμησης των όζων και την παροχή βοήθειας στους ιατρούς κατά την

προ-εγχειρητική αντιμετώπιση των ασθενών.

Η παρούσα διατριβή πραγματεύεται τον σχεδιασμό, την ανάπτυξη και υλοποίηση νέων μεθόδων:

1. Επεξεργασίας εικόνας βασισμένες στον μετασχηματισμό μικροκυματιδίων (Wavelet

Transform) με σκοπό την αφαίρεση θορύβου και την τμηματοποίηση των όζων.

2. Ανάλυσης εικόνας με σκοπό την αυτόματη ταξινόμηση των όζων σε όζους υψηλού και

χαμηλού κινδύνου.

1. Μέθοδοι Επεξεργασίας Εικόνας με βάση τον Wavelet

Transform (WT)

1.1 Εισαγωγή

Παρά τα μεγάλα πλεονεκτήματα της υπερηχογραφίας, στις εικόνες εμφανίζεται μια κοκκώδης

υφή η οποία αποτελεί έναν σημαντικό παράγοντα υποβάθμισης της ποιότητας εικόνας. Όταν μια

δέσμη υπερήχων προσπίπτει σε μια ανομοιογενή επιφάνεια ή σε σωματίδια με μέγεθος ή

αποστάσεις μεταξύ τους μικρότερες από το όριο της χωρικής διακριτικής ικανότητας του

συστήματος, παρουσιάζονται φαινόμενα συμβολής (αφαιρετικής και ενισχυτικής) με αποτέλεσμα

τόσο την παραμόρφωση των ανατομικών δομών όσο και την διαφοροποίηση στην ένταση των

ανακλώμενων από αυτές ηχητικών κυμάτων (διαφοροποίηση των τόνων του γκρι). Οι έντονες

αυτές διακυμάνσεις στην ένταση των ανακλώμενων κυμάτων μέσα σε μια ομοιόμορφη

ανατομική περιοχή συνθέτουν το speckle [90,111]. Η υπερηχογραφική εικόνα με την παρουσία

του speckle πολλές φορές δεν αντιστοιχεί στην πραγματική δομή των εικονιζόμενων ιστών. Το

speckle υποβαθμίζει τις μικρές λεπτομέρειες και τον σαφή καθορισμό των οριογραμμών της

περιοχής ενδιαφέροντος. Επιπλέον, αποτελεί έναν περιοριστικό παράγοντα για τον σχεδιασμό

αλγορίθμων τμηματοποίησης και αναγνώρισης προτύπων.

III

Εκτός της παρουσίας του speckle, διάφορες ιδιότητες των υπερηχητικών κυμάτων μπορούν να

προκαλέσουν την ποιοτική υποβάθμιση και ενδεχομένως ψευδείς ενδείξεις στις εικόνες

υπερηχογραφίας. Η αντήχηση, η σκίαση, η διάθλαση και οι πλευρικοί λοβοί υποβαθμίζουν την

διακριτική ικανότητα της απεικόνισης και κατά συνέπεια την συνολική ποιότητά της [47,49]. Τα

προαναφερθέντα προβλήματα που προκύπτουν από τη σύνθετη φύση της υπερηχογραφικής

απεικόνισης, καθιστούν την ακριβή ανίχνευση των ορίων μιας συγκεκριμένης ανατομικής δομής

αρκετά δύσκολη ακόμα και για τους ακτινολόγους με μεγάλη πείρα. Ένας ακριβής υπολογισμός

του περιγράμματος ενός όζου του θυρεοειδούς αποτελεί καθοριστικό παράγοντα τόσο στον

εντοπισμό του μεγέθους και της θέση του όζου όσο και στην ταξινόμηση των όζων με βάση

διάφορα μορφολογικά χαρακτηριστικά. Επιπλέον, μπορεί βοηθήσει στην ακριβή τοποθέτηση της

βελόνας βιοψίας σε πραγματικό χρόνο κατά την διαδικασία της FNAB [29-33].

Οι περισσότεροι σύγχρονοι αλγόριθμοι επεξεργασίας εικόνας δεν είναι αποτελεσματικοί όταν

εφαρμόζονται απευθείας στις τιμές έντασης των τόνων του γκρι της υπερηχογραφικής εικόνας.

Αυτές οι τιμές έντασης είναι ιδιαίτερα πλεονάζουσες, ενώ το ποσοστό σημαντικών πληροφοριών

μέσα στην εικόνα μπορεί να είναι σχετικά μικρό. Η απεικόνιση των τόνων του γκρι υπό μια

διαφορετική γωνία μπορεί να αναδείξει διάφορα σημαντικά χαρακτηριστικά γνωρίσματα που δεν

είναι ευδιάκριτα στην αρχική εικόνα. Ο μετασχηματισμός με βάση τα μικροκυματίδια (wavelet

transform) της αρχικής υπερηχογραφικής εικόνας σε μια απεικόνιση χαρακτηριστικών

αποκαλύπτει τα χρήσιμα γνωρίσματα μιας εικόνας χωρίς την απώλεια ουσιαστικών

πληροφοριών, μειώνει τον πλεονασμό των διάφορων τόνων του γκρι και αποβάλλει

οποιεσδήποτε μη χρήσιμες πληροφορίες [55].

Όταν σε μια εικόνα οι σημαντικές δομές έχουν διαφορετικά μεγέθη, οι κλίμακες πρέπει να

ποικίλουν. Οι αιχμές σε διάφορες κλίμακες αντιστοιχούν σε διαφορετικές φυσικές οντότητες. Τα

μεγάλα αντικείμενα απεικονίζονται με ακρίβεια στις μεγάλες κλίμακες ενώ οι μικρές δομές

εντοπίζονται ευκολότερα στις μικρές κλίμακες. Ο μετασχηματισμός μικρο-κυματιδίων σε

πολλαπλές κλίμακες παρέχει την δυνατότητα μελέτης και ανάλυσης διαφόρων αιχμών

μεταβάλλοντας το μέγεθος του οπτικού παραθύρου εξέτασης [57,58].

Οι Mallat και Zong [62] έχουν αποδείξει ότι η απεικόνιση των αιχμών σε διαφορετικές κλίμακες

παρέχει μια πλήρη και σταθερή αντιπροσώπευση της αρχικής εικόνας, γεγονός το οποίο σημαίνει

ότι το σύνολο των πληροφοριών της εικόνας υπάρχει σε αυτές τις αιχμές. Η διαπίστωση αυτή

υποδηλώνει ότι οι διάφορες μέθοδοι επεξεργασίας εικόνας μπορούν να χρησιμοποιηθούν

απευθείας στην απεικόνιση των αιχμών αντί στην αρχική εικόνα.

Οι διάφορες αιχμές ή τα περιγράμματα (ομάδες αιχμών με παρόμοιες ιδιότητες) αντιστοιχούν

στις έντονες αντιθέσεις των τόνων του γκρι και μπορούν να αντιπροσωπευθούν από τα τοπικά

IV

μέγιστα της μετατροπής μικρο-κυματιδίων. Η αναπαράσταση τοπικών μεγίστων είναι μια

αναδιοργάνωση των πληροφοριών της εικόνας, η οποία παρέχει με μεγαλύτερη ανάλυση την

απεικόνιση διαφόρων δομών.

Μια ξεχωριστή ιδιότητα του μετασχηματισμού μικροκυματιδίων (WT) είναι η ικανότητα του να

χαρακτηρίζει την τοπική κανονικότητα διαφόρων χαρακτηριστικών της εικόνας όπως ασυνέχειες

ή έντονες αιχμές. Η τοπική κανονικότητα υπολογίζεται μέσω των εκθετών Lipschitz [61]. Η

απεικόνιση των αιχμών σε διάφορες κλίμακες παρέχει τη δυνατότητα της ανίχνευσης των

διαφόρων ιδιομορφιών (singularities – σημεία στον χώρο όπου λαμβάνουν χώρα απότομες

μεταβολές) που βρίσκονται σε μια εικόνα και του υπολογισμού της κανονικότητας τους. Σε

αυτήν την διατριβή πραγματοποιήθηκε μια έρευνα σχετικά με την συμπεριφορά των ιδιομορφιών

(singularities) σε μια υπερηχογραφική εικόνα του θυρεοειδούς αδένα υπολογίζοντας την

Lipschitz κανονικότητα τους. Τα τοπικά μέγιστα που δημιουργούνται από τις ιδιομορφίες

(singularities) που αντιστοιχούν σε θόρυβο έχουν διαφορετική συμπεριφορά από αυτά που

επηρεάζονται κυρίως από τις ωφέλιμα χαρακτηριστικά της εικόνας.

Η έρευνα κατέληξε στην διαπίστωση ότι η κατανομή του speckle – το μοντέλο θορύβου το οποίο

υιοθετήθηκε σε αυτήν την διατριβή θεωρεί το speckle σαν έναν αθροιστικό παράγοντα, άμεσα

εξαρτώμενο από το αρχικό σήμα – είναι σχεδόν παντού σημειακή (singular) ή ασυνεχής με μη

θετικούς εκθέτες Lipschitz. Αντιθέτως, οι χρήσιμες ιδιομορφίες (singularities) που προέρχονται

από την φυσιολογική κατανομή των τόνων του γκρι στην υπερηχογραφική εικόνα αποτελούν

έντονες αιχμές με θετικούς εκθέτες Lipschitz.

1.2 Αφαίρεση Θορύβου στις Υπερηχογραφικές Εικόνες

1.2.1 Εισαγωγή

Σαν εφαρμογή της προαναφερθείσας διαπίστωσης, ένας αλγόριθμος αναπτύχθηκε η οποίος

αφαιρεί το speckle από τις υπερηχογραφικές εικόνες υπερήχου με την ανάλυση της βαθμιαίας

εξέλιξης των τοπικών μεγίστων στις διάφορες κλίμακες. Αυτή η αναζήτηση πραγματοποιήθηκε

με τον εντοπισμό των αιχμών στις μεγάλες κλίμακες και την προοδευτική ανίχνευση τους προς

την μικρότερη δυνατή κλίμακα ώστε μελετηθεί η συμπεριφορά τους.

Στην διεθνή βιβλιογραφία έχει εφαρμοσθεί πληθώρα μεθόδων για την αφαίρεση του speckle σε

εικόνες υπερηχογραφίες διαφόρων ανατομικών δομών. Οι πρώτες μέθοδοι χρησιμοποίησαν

διάφορες παραμέτρους από το ιστόγραμμα της εικόνας για την αφαίρεση του speckle [92,93,94].

Στην δεκαετία του 1990 η αύξηση της υπολογιστικής ισχύος των Η/Υ προκάλεσε την ταυτόχρονη

αύξηση της πολυπλοκότητας των φίλτρων για την καταστολή του speckle. Οι μέθοδοι

V

εφαρμόζονταν κατά βάση στο πεδίο του χρόνου [95-100]. Επίσης, στο δεύτερο μισό της

δεκαετίας του ’90 καινούργιες μέθοδοι προτάθηκαν με βάση τον μετασχηματισμό

μικροκυματιδίων [101-103].

1.2.2 Μέθοδοι

Η τεχνική αφαίρεσης θορύβου περιλαμβάνει τα ακόλουθα βήματα:

1. Δυαδικός Μετασχηματισμός μικροκυματιδίων (Dyadic Wavelet Transform)

2. Αναπαράσταση Τοπικών Μεγίστων (Modulus maxima representation)

3. Ομαδοποίηση των τοπικών μεγίστων από την μεγαλύτερη στην μικρότερη κλίμακα του

μετασχηματισμού (Coarse to fine grouping of local maxima)

4. Υπολογισμός κανονικότητας Lipschitz (Lipschitz regularity calculation)

5. Αντίστροφος Δυαδικός Μετασχηματισμός μικροκυματιδίων (Inverse Dyadic Wavelet

Transform)

1. Δυαδικός Μετασχηματισμός μικροκυματιδίων: Η ανάλυση μικροκυματιδίων που

παρουσιάζεται σε αυτήν την διατριβή χρησιμοποιεί τον Δυαδικό Μετασχηματισμό

μικροκυματιδίων για το χαρακτηρισμό των σημάτων από τις αιχμές σε διάφορες κλίμακες

(Multiscale Edge Representation) [62]. Η ανάλυση μικροκυματιδίων σε διάφορες κλίμακες της

αρχικής εικόνας εφαρμόστηκε με μια τράπεζα φίλτρων η οποία αποκαλείται ως `algorithme a

atrous’ (αλγόριθμος με τρύπες) [63].

2. Αναπαράσταση Τοπικών Μεγίστων: O δυσδιάστατος μετασχηματισμός

μικροκυματιδίων μιας εικόνας μπορεί να θεωρηθεί σαν ένα άνυσμα κλίσης το οποίο μπορεί να

αναπαρασταθεί από το μέτρο και τη γωνία του. Ένα σημείο θεωρείται ως τοπικό μέγιστο εάν το

πλάτος του ανύσματος κλίσης είναι μεγαλύτερο έναντι των γειτονικών του κατά μήκος της

κατεύθυνσης που δίνεται από τη γωνία του [62,66].

3. Ομαδοποίηση των τοπικών μεγίστων από την μεγάλη στην μικρή κλίμακα του

μετασχηματισμού: Στην παρούσα μελέτη η πληροφορία η οποία βρίσκεται στις διαφορετικές

ζώνες συχνότητας (κλίμακες) αναλύεται ώστε να υπολογιστεί η τοπική κανονικότητα των

χαρακτηριστικών της εικόνας. Αυτές οι πληροφορίες στις διάφορες κλίμακες υπολογίζονται

μέσω μια διαδικασίας ανίχνευσης τοπικών μεγίστων με κοινές ιδιότητες τα οποία διαδίδονται

από την τελευταία κλίμακα μέχρι την πρώτη (Back-propagation Tracking). Η ομαδοποίηση των

τοπικών μεγίστων σε όλες τις διαθέσιμες κλίμακες βασίζεται στην αρχή ότι: εάν μια αιχμή

υπάρχει σε ένα μεγαλύτερο επίπεδο j2 , μπορεί επίσης να εντοπιστεί σε ένα μικρότερο επίπεδο

VI

12 −j . Δύο τοπικά μέγιστα από δύο διαδοχικές κλίμακες ομαδοποιούνται εάν κατέχουν κοντινές

θέσεις και γωνίες στο επίπεδο της εικόνας [68,69].

4. Υπολογισμός κανονικότητας Lipschitz: Η διακύμανση του πλάτους των τοπικών

μεγίστων σε διαφορετικές κλίμακες συσχετίζεται με την τοπική κανονικότητα των αντίστοιχων

δομών που αντιπροσωπεύουν τα τοπικά μέγιστα. Η κλίση της καμπύλης των τοπικών μεγίστων

σε λογαριθμική κλίμακα αποτελεί την κανονικότητα αυτών των μεγίστων και αξιολογείται μέσω

των εκθετών Lipschitz "α". Όταν το πλάτος των τοπικών μεγίστων σε μια ομάδα μειώνεται όσο

μειώνεται και η κλίμακα η κανονικότητα Lipschitz είναι θετική (θετικοί εκθέτες Lipschitz). Όταν

το πλάτος των τοπικών μεγίστων σε μια ομάδα αυξάνεται όσο μειώνεται η κλίμακα η

κανονικότητα Lipschitz είναι αρνητική (αρνητικοί εκθέτες Lipschitz). Το speckle αντιστοιχεί σε

αρνητικούς εκθέτες Lipschitz ενώ οι διάφορες δομές της υπερηχογραφικής εικόνας αντιστοιχούν

σε θετικούς εκθέτες Lipschitz [68-71].

5. Αντίστροφος Δυαδικός Μετασχηματισμός μικροκυματιδίων: Η διάκριση των

τοπικών μεγίστων που αντιστοιχούν σε speckle ή σε κανονικές δομές της υπερηχογραφικής

εικόνας βασίζεται στον πρόσημο των εκθετών Lipschitz. Οι συντελεστές του μετασχηματισμού

που αντιστοιχούν στα μέγιστα με τους αρνητικούς εκθέτες Lipschitz μηδενίζονται. Οι υπόλοιποι

συντελεστές χρησιμοποιούνται στον αντίστροφο μετασχηματισμό για την δημιουργία της εικόνας

χωρίς speckle.

1.2.3 Αποτελέσματα

Η αποτελεσματικότητα της προτεινόμενης μεθόδου με βάση τον μετασχηματισμό

μικροκυματιδίων αξιολογήθηκε μέσω ενός ομοιώματος ανθρώπινων ιστών και μιας

υπερηχογραφικής εικόνας του θυρεοειδούς αδένα. Η προτεινόμενη μέθοδος (Inter-scale wavelet

speckle suppression) συγκρίθηκε με τρεις αντιπροσωπευτικές μεθόδους αφαίρεσης θορύβου σε

εικόνες υπερηχογραφίας: (α) Adaptive speckle suppression filter (ASSF) [97], (β) Soft

Thresholding [104] και (γ) Hard thresholding [104]. Τα αποτελέσματα της αξιολόγησης έδειξαν

ότι η προτεινόμενη μέθοδος ήταν ανώτερη έναντι των υπολοίπων με βάση τους παρακάτω

δείκτες: speckle index και signal-to-mean-square-error ratio για την απόδοση του αλγορίθμου

στην μείωση του speckle και την παράμετρο – β –για την ταυτόχρονη διατήρηση των αιχμών και

του περιγράμματος των διαφόρων δομών (Πίνακας 1.1).

VII

Πίνακας 1.1 Δείκτες ποιότητας υπερηχογραφικής εικόνας από τις τέσσερις μεθόδους αφαίρεσης

speckle σε εικόνα υπερηχογραφίας/ομοίωμα ανθρώπινου ιστού

Μέθοδος SI (Ποσοστιαία βελτίωση)

S/mse (dB) β (dB)

ASSF 14% / 12% 10.5664 / 12.7728 0.3592 / 0.1458

Soft Thresholding 19% / 18% 14.5472 / 16.7709 0.7063 / 0.7453

Hard Thresholding 16% / 15% 11.4083 / 15.1853 0.7836 / 0.8013

Inter-scale wavelet speckle suppression

23% / 21% 16.2937 / 18.3241 0.8490 / 0.8485

Επίσης υλοποιήθηκε μια μελέτη αξιολόγησης της μεθόδου από δύο παρατηρητές

περιλαμβάνοντας 63 εικόνες υπερηχογραφίας θυρεοειδή 63 ασθενών μέσω ενός

ερωτηματολογίου σχετικά με την απόδοση του προτεινόμενου αλγορίθμου. Το ερωτηματολόγιο

περιλάμβανε επτά ερωτήσεις με διάφορες οπτικές παρατηρήσεις σχετικά με την προτεινόμενη

αποτελεσματικότητα του αλγορίθμου. Οι απαντήσεις των παρατηρητών – Ιατρών ήταν απόλυτα

συνυφασμένες με την ποσοτική αξιολόγηση της μεθόδου. Πρέπει να σημειωθεί ότι και οι δύο

Ιατροί στο σύνολο των εικόνων παρατήρησαν ότι η τεχνική αφαίρεσης του speckle είχε μια

ιδιαιτέρως ικανοποιητική επίδραση στην ποιότητα της υπερηχογραφικής εικόνας αυξάνοντας την

διακριτική ικανότητα και την αντίθεση των εικονιζόμενων δομών. Επίσης είναι χαρακτηριστικό

ότι παρά την αφαίρεση του speckle στο σύνολο της εικόνας, οι διάφορες αιχμές που υπήρχαν στις

εικόνες δεν επηρεάστηκαν καθόλου από την εφαρμογή του αλγορίθμου.

1.2.4 Συμπεράσματα

Σαν τελικό συμπέρασμα μπορούμε να πούμε ότι υλοποιήθηκε μια αποτελεσματική μέθοδος

αφαίρεσης του speckle σε εικόνες υπερηχογραφίας. Αυτή η μέθοδος βασίστηκε στον

μετασχηματισμό μικροκυματιδίων, στην οποία ο πρωταρχικός στόχος ήταν να απομονωθούν οι

αιχμές που υπάρχουν στις διάφορες κλίμακες και να ελεγχθεί η κανονικότητα τους. Η επιτυχής

καταστολή του θορύβου από τον προτεινόμενο αλγόριθμο μπορεί να υιοθετηθεί ως ένα βήμα

προ-επεξεργασίας για την τμηματοποίηση των όζων και σαν ένα βοηθητικό εργαλείο στη

βελτίωση της συνολικής διαγνωστικής διαδικασίας.

VIII

1.3 Τμηματοποίηση των όζων του θυρεοειδούς αδένα

1.3.1 Εισαγωγή

Οι ιδιότητες των αιχμών στις διάφορες κλίμακες με βάση της κανονικότητα τους

χρησιμοποιήθηκαν επίσης ως δεδομένα σε ένα υβριδικό μοντέλο για την αυτόματη

τμηματοποίηση των όζων του θυρεοειδούς αδένα

Πολυάριθμες αυτόματες ή ημι-αυτόματες μέθοδοι τμηματοποίησης έχουν παρουσιαστεί στην

διεθνή αρθρογραφία σε εικόνες υπερηχογραφίας του προστάτη, των νεφρών, της καρδιακής

ανατομίας, των ωοθηκών, του εμβρυϊκού κρανίου και των εικόνων μαστού. Όλοι αυτοί οι

αλγόριθμοι μπορούν να ταξινομηθούν χονδρικά σε πέντε κατηγορίες ανάλογα με τη στρατηγική

που επιλέγεται για την τμηματοποίηση της εκάστοτε περιοχής ενδιαφέροντος (ROI). Οι μέθοδοι

αυτές τμηματοποίησης βασίζονται:

(α) στην ανίχνευση αιχμών [118,123],

(β) στην ανάλυση χαρακτηριστικών υφής [124–130],

(γ) σε διάφορα μοντέλα (deformable and active models) [131,141],

(δ) σε συνδυασμό των προαναφερθέντων [142–145],

(ε) στον μετασχηματισμό μικροκυματιδίων σε διάφορες κλίμακες [146–159].

1.3.2 Μέθοδοι

Η προτεινόμενη μέθοδος ενσωματώνει στο υβριδικό μοντέλο, τον μετασχηματισμό

μικροκυματιδίων για την ανίχνευση αιχμών (Edge Detection), με τελικό σκοπό την ταυτόχρονη

στερεοσκοπική ανίχνευση της συγκεκριμένης ανατομικής δομής σε όλες τις κλίμακες. Ο τελικός

χάρτης περιγράμματος, που προέρχεται από το μοντέλο, χρησιμεύει σαν είσοδος στον

μετασχηματισμό Hough με σκοπό την τελική τμηματοποίηση των όζων. Τα βήματα της μεθόδου

είναι τα εξής:

1. Ανίχνευση αιχμών στο σύνολο των κλιμάκων του μετασχηματισμού (Edge detection

procedure)

2. Ανίχνευση δομών σε όλες τις κλίμακες του μετασχηματισμού (Multi-scale structure model)

3. Εξαγωγή του περιγράμματος του όζου (Nodule’s boundary extraction)

1. Ανίχνευση αιχμών στο σύνολο των κλιμάκων του μετασχηματισμού. Η διαδικασία

ανίχνευσης αιχμών βασίζεται στον μετασχηματισμό μικροκυματιδίων σε διάφορες δυαδικές

κλίμακες. Ο τελικός χάρτης των αιχμών υπολογίζεται αναλύοντας τα τοπικά μέγιστα από την

μεγαλύτερη στην μικρότερη κλίμακα του μετασχηματισμού. Τα τοπικά μέγιστα με θετικούς

εκθέτες ` lipschitz " εισάγονται στο μοντέλο ανίχνευσης δομών που ακολουθεί. Τα τοπικά

IX

μέγιστα με τους αρνητικούς εκθέτες lipschitz ταξινομούνται ως speckle και αφαιρούνται από την

συνέχεια της επεξεργασίας.

2. Ανίχνευση δομών στο σύνολο των κλιμάκων του μετασχηματισμού. Το επόμενο βήμα

αυτής της μεθόδου είναι η ανίχνευση δομών σε όλες τις κλίμακες του μετασχηματισμού, η οποία

θα συνέδεε μια ανατομική δομή στην υπερηχογραφική εικόνα με μια στερεοσκοπική

αναπαράσταση της δομής αυτής με βάση τα τοπικά μέγιστα του μετασχηματισμού. Οι βασικές

συνιστώσες του προτεινόμενου μοντέλου είναι:

(α) τα τοπικά μέγιστα από το 1ο βήμα,

(β) οι αλυσίδες τοπικών μεγίστων που αποτελούν ομάδες τοπικών μεγίστων με παρόμοιες

ιδιότητες στην ίδια κλίμακα,

(γ) οι ανατομικές δομές που απαρτίζουν ένα σύνολο συνδεδεμένων αλυσίδων τοπικών μεγίστων,

(δ) η σχέση που υπάρχει στο σύνολο των κλιμάκων για τον καθορισμό των κριτηρίων που

υιοθετούνται από τον αλγόριθμο ώστε οι ομάδες αυτές να ενοποιηθούν για τον σχηματισμός της

δομής

(ε) και ένας αριθμητικός τελεστής ο οποίος αντιστοιχεί σε ποια δομή ανήκουν οι διάφορες

ομάδες αλυσίδων τοπικών μεγίστων.

Ο συνδυασμός αυτών των συνιστωσών υλοποιεί το μοντέλο για την όσο το δυνατόν

αντιπροσωπευτικότερη παρουσίαση του περιγράμματος του όζου.

3. Εξαγωγή του περιγράμματος του όζου. Για την τελική τμηματοποίηση του όζου, η

έξοδος του μοντέλου εισάγεται στον μετασχηματισμό Hough ο οποίος έχει την δυνατότητα της

μερική αναγνώριση κοίλων αντικειμένων σε ένα περιβάλλον με μεγάλο θόρυβο από

παρακείμενες δομές. Ο μετασχηματισμός Hough έχει την δυνατότητα να ανιχνεύει δομές ακόμα

και αν το περίγραμμα αυτών δεν είναι συνεχές.


Για την αξιολόγηση της απόδοσης της προτεινόμενης μεθόδου τμηματοποίησης, μια συγκριτική

μελέτη υλοποιήθηκε, περιλαμβάνοντας 40 εικόνες υπερηχογραφίας του θυρεοειδή αδένα από 40

ασθενείς μεταξύ 40 και 65 ετών. Όλες οι εικόνες επιλέχτηκαν τυχαία από μια μεγάλη βάση

δεδομένων. Τα αποτελέσματα τμηματοποίησης της μεθόδου συγκρίθηκαν με βάση με την

χειροκίνητη σκιαγράφηση των όζων (θεωρούμενη ως ground truth) που προήλθαν από δύο

έμπειρους παρατηρητές (OB1 και OB2) και με βάση κάποια μορφολογικά χαρακτηριστικά όπως

το εμβαδόν, η σφαιρικότητα (roundness), η κοιλότητα (concavity) και η μέση απόλυτη απόσταση

μεταξύ των περιγραμμάτων της μεθόδου και των δύο παρατηρητών (Mean Absolute Distance).

X

Στη συγκριτική μελέτη, η ακρίβεια τμηματοποίησης των όζων του θυρεοειδούς προσέγγισε

ποσοστά ταύτισης των περιγραμμάτων με τους δύο παρατηρητές της τάξης των 90,14 και

89,33%. Το ποσοστό ταύτισης της μεθόδου με τα αποτελέσματα των δύο παρατηρητών είναι

εφάμιλλο με το ποσοστό ταύτισης μεταξύ των δύο παρατηρητών (91,83%) (Πίνακας 2.1).

Πίνακας 1.2 Μέση ποσοστιαία συμφωνία μεταξύ της αυτόματης μεθόδου (AU) και την

χειροκίνητης μεθόδου τμηματοποίησης από τους δύο παρατηρητές (OB1, OB2) σε σχέση με το

εμβαδόν, την στρογγυλότητα, Κοιλότητα και MAD% .

Εμβαδόν Στρογγυλότητα Κοιλότητα MAD%

AU- OB1

AU- OB2

AU- OB1

AU- OB2

AU- OB1

AU- OB2

AU- OB1

AU- OB2

Μέση Ποσοστιαία Συμφωνία 88,83

87,58

91,77 91,12 89,21 89,08 90,77 89,53

Η inter-observer μελέτη κατέδειξε την υψηλή συμφωνία συντελεστή kappa περίπου 0,83. Αν και

ο αλγόριθμος είναι αυτόματος, τα αποτελέσματα αξιολόγησης μπορούν να θεωρηθούν αρκετά

ενθαρρυντικά πάντα σε σχέση με την εν γένει χαμηλή ποιότητα γένει της υπερηχογραφικής

εικόνας. Ο προτεινόμενος αλγόριθμος μπορεί να αποτελέσει ένα πρωτεύων εργαλείο σε

συστήματα αυτόματης διάγνωσης για την ταξινόμηση των όζων αλλά και ως ένα δευτερεύων

εργαλείο κατά την ίδια την υπερηχογραφική εξέταση.


Σαν συμπέρασμα, μια νέα τεχνική τμηματοποίηση όζων του θυρεοειδούς αδένα προτείνεται με

αρκετά καλά αποτελέσματα. Ο προτεινόμενος αλγόριθμος είναι σε θέση να ανιχνεύσει τους

όζους ανεξαρτήτως ηχογένειας και πιθανής ύπαρξης ασυνέχειας στο περίγραμμα του όζου.

Επίσης κατορθώνει και εξάγει την περιοχή ενδιαφέροντος ανεξαρτήτου του ποσοστού δομικού

θορύβου από παρακείμενες δομές. Η χρησιμοποίηση της υβριδικής μεθόδου μπορεί να βοηθήσει

στην κατηγοριοποίηση των όζων από τον παθολόγο και να ενισχύσει την ακρίβεια της

διαδικασίας λήψης βιοψίας (FNAB). Επιπλέον μπορεί να χρησιμοποιηθεί ως εκπαιδευτικό

εργαλείο για τους άπειρους ακτινολόγους.

XI

2. Αυτόματη διάγνωση των όζων του θυρεοειδούς αδένα

2.1 Εισαγωγή Οι όζοι αναπτύσσονται από τα θυλακιώδη κύτταρα του θυρεοειδούς και απαντώνται στους

θυρεοειδείς αδένες φυσιολογικού μεγέθους και στους διογκωμένους θυρεοειδείς αδένες

(βρογχοκήλες). Το 95% των όζων του θυρεοειδούς αδένα είναι καλοήθεις. Μόνο ένα μικρό

ποσοστό των όζων ταξινομείται σαν κακοήθεις. Υπάρχουν διάφορες μορφές του καρκίνου του

θυρεοειδούς: Θηλώδες καρκίνωμα (Papillary carcinoma – 75%), Θυλακιώδες ή λεμφοζιδιακό

καρκίνωμα (follicular carcinoma – 15%, Σε αυτήν την περίπτωση η χρήση της έγχρωμης

απεικόνισης Doppler βοηθά στην διάγνωση), Μυελλοειδές καρκίνωμα (Medullary carcinoma –

7%), Αναπλαστικό καρκίνωμα (Anaplastic carcinoma – 3%) . Στους νέους ανθρώπους αν η

διάγνωση είναι έγκαιρη, το ποσοστό ίασης του Θηλώδους και Θηλακιώδους καρκινώματος

αγγίζει το 95%. Στις άλλες δύο περιπτώσεις η ακρίβεια πρόγνωσης είναι μικρή. Ωστόσο, η

ακριβής εκτίμηση και ταξινόμηση των κακοήθων όζων, εξαιτίας της φύσεως της

υπερηχογραφικής εικόνας, παραμένει μια δύσκολη απόφαση [1-12].

Η μέτρηση του μεγέθους, της θέσης αλλά και άλλων χαρακτηριστικών (περιγράμματος και

εσωτερικής μορφολογίας) του κάθε όζου μέσα από την εικόνα υπερηχογραφίας βοηθά στην

σωστή αξιολόγηση του από τον ιατρό. Άλλες παράμετροι της εικόνας, όπως η παρουσία

ηχοδιαυγαστικής ζώνης (άλω) που περιβάλει τους χαμηλού κινδύνου όζους και η παρουσία

αποτιτανώσεων σε υψηλού κινδύνου όζους βοηθούν στην προσέγγιση της διάγνωσης.

Οι συμπαγείς όζοι του θυρεοειδούς αδένα, σε ένα μεγάλο ποσοστό, δεν είναι δυνατόν να

ταξινομηθούν αυστηρά σε καλοήθεις ή κακοήθεις με τις διάφορες απεικονιστικές μεθόδους που

εφαρμόζονται σήμερα (Υπερηχογραφική εικόνα, γ-κάμερα), με αποτέλεσμα οι ασθενείς να

υποβάλλονται σε βιοψία για κυτταρολογική εξέταση από διάφορες περιοχές του όζου [1]. Η

δημοφιλέστερη τεχνική λήψης κυτταρολογικού υλικού (βιοψία) από το θυρεοειδή είναι η Fine

Needle Aspiration λόγω της υψηλής ακρίβειας διάγνωσης, ασφάλειας και μικρού κόστους

εξέτασης. Το κυτταρολογικό υλικό που λαμβάνεται μέσω της FNA τοποθετείται σε γυάλινα

πλακάκια μικροσκοπίου και κατόπιν εξετάζεται από τον παθολογοανατόμο μέσω συστημάτων

μικροσκοπίας.

Η εξέταση στο πλακάκι μικροσκοπίας αποτελεί το τελευταίο στάδιο της διαγνωστικής αλυσίδας

είτε για την αναγνώριση τόσο των καλοηθών από τους κακοήθεις όζους είτε του βαθμού

επικινδυνότητας των όζων. Η διεθνής βιβλιογραφία έχει αναδείξει την κυτταρολογική εξέταση

ως τη σημαντικότερη για τον εντοπισμό και την ταξινόμηση των όζων του θυρεοειδούς με

ακρίβεια αναγνώρισης που ξεπερνάει το 85%. Αποκλείοντας τις σπάνιες περιπτώσεις του

XII

χαρακτηριστικού νεοπλάσματος του θυρεοειδή η κυτταρολογική εκτίμηση διαχωρίζει του όζους

σε δύο σημαντικές κατηγορίες: (α) επιθηλιακή υπερπλασία που μπορεί να χαρακτηριστεί ως

υψηλού κινδύνου με πιθανή εμφάνιση κακοήθειας έχοντας ως αποτέλεσμα τις

επαναλαμβανόμενες εξετάσεις υπερήχου και κυτταρολογίας του ασθενή, και (β) στις καλοήθεις

περιοχές (κολλοειδείς όζοι), όπου οι υπερηχογραφικές εξετάσεις μπορούν να πραγματοποιηθούν

ανά μεγάλα χρονικά διαστήματα. Η ανάγκη για την όσο τον δυνατόν πιο αντικειμενική εκτίμηση

και ανάδειξη των υπερηχογραφικών χαρακτηριστικών που εμφανίζει η κάθε μια κατηγορία

οδήγησε στην ανάγκη σχεδιασμού και υλοποίησης ενός αυτόματου συστήματος ταξινόμησης των

όζων στις δύο αυτές κατηγορίες.

Υπάρχουν δημοσιευμένες μελέτες σχετικά με την υλοποίηση αυτόματων προγραμμάτων

διάγνωσης του πιθανότητας εμφάνισης κακοήθειας όζων του θυρεοειδούς αδένα. Αυτές οι

μελέτες βασίζονται κυρίως σε χαρακτηριστικά από το ιστόγραμμα της υπερηχογραφικής εικόνας

[164,165], διάφορα χαρακτηριστικά υφής [166] και στην εφαρμογή ανάλυσης διαχωρισμού

(discriminant analysis) [164-166]. Σε εκείνες τις μελέτες, τα ποσοστά διαχωρισμού μεταξύ των

καλοηθών και των κακοήθων όζων ήταν 83,9% [166] και 85% [164].

Σε αυτήν μελέτη περιλαμβάνονται ασθενείς με όζους του θυρεοειδούς αδένα που εξετάσθηκαν σε

ένα υπερηχογραφικό σύστημα και στη συνέχεια υποβλήθηκαν σε διαγνωστική βιοψία με τη

μέθοδο FNA στην ιδιωτική κλινική EUROMEDICA. Τα βασικά βήματα της μελέτης είναι:

1. Συλλογή εικόνων υπερηχογραφίας από ασθενείς με όζους του θυρεοειδούς και δημιουργία

ψηφιακής βάσης δεδομένων για την καταγραφή ιστορικού ασθενούς και κλινικών

δεδομένων.

2. Σχεδιασμός-προτυποποίηση παραμέτρων λήψης εικόνας. Πραγματοποιήθηκε έλεγχος

ποιότητας του υπερηχογραφικού συστήματος από την εταιρία κατασκευής.

3. Ανάλυση υπερηχογραφικών εικόνων για την δημιουργία χαρακτηριστικών (υφής,

περιγράμματος και τοπικών μεγίστων) του όζου με τη βοήθεια στατιστικών παραμέτρων

(στατιστικές παράμετροι πρώτης, δεύτερης [170] και ανώτερης τάξης [73,74] κ.α. Επιλογής

χαρακτηριστικών με μεθόδους μονομεταβλητής και πολυμεταβλητής στατιστικής ανάλυσης

[70, 83, 170].

4. Ταξινόμηση των όζων του θυρεοειδούς σε δύο βασικές (υψηλού κινδύνου – χαμηλού

κινδύνου) με την υλοποίηση κλασσικών ταξινομητών, Μηχανών Υποστήριξης Διανυσμάτων

(SVM) και Πιθανοκρατικών Νευρωνικών Δικτύων (PNN).

XIII

2.2 Υπολογιστικό Σύστημα Αναγνώρισης Προτύπων βασισμένο σε

Χαρακτηριστικά Υφής

2.2.1 Βάση Δεδομένων

Υπερηχογραφικές εικόνες από 120 διαφορετικούς ασθενείς, οι οποίοι έχουν ηλικία από 30 έως 75

ετών και ανήκουν και στα δύο φύλα συλλέχθηκαν στο χρονικό διάστημα από τον Οκτώβριο του

2003 μέχρι τον Σεπτέμβριο του 2004 από τον ιατρικό διαγνωστικό κέντρο EUROMEDICA,

Κατεχάκη 4, Αθήνα, Ελλάδα. Το Υπερηχογραφικό σύστημα απεικόνισης το οποίο

χρησιμοποιήθηκε για την απόκτηση των εικόνων είναι ο υπερηχοτομογράφος HDI 3000 ATL-

PHILΙPS (PHILIPS, USA). Ο υπεύθυνος ιατρός που πραγματοποιεί τις εξετάσεις είναι ο Δρ.

Νίκος Δημητρόπουλος. Οι εικόνες που αποκτήθηκαν είναι δισδιάστατες με 256 τόνους του γκρι,

ενώ η χρησιμοποιούμενη ηλεκτρονική κεφαλή είναι γραμμικής διάταξης (Linear Array) και

κεντρικής συχνότητας συντονισμού 7 MHz με δυνατότητα ανίχνευσης ενός εύρους συχνοτήτων

γύρω από την ονομαστική (5-9 ΜΗz - Broadband). Για την βέλτιστη απεικόνιση του όζου

λαμβάνονται διάφορες εικόνες από τον ίδιο όζο σε εγκάρσιο, οβελιαίο και πρόσθιο επίπεδο. Για

την ψηφιοποίηση του σήματος Video του υπερηχογράφου χρησιμοποιήσαμε την κάρτα Video,

Miro PCTV (Pinnacle Systems), η οποία είναι εγκατεστημένη σε έναν Η/Υ.

Διάφορα χαρακτηριστικά υφής υπολογίστηκαν αυτόματα από την περιοχή ενδιαφέροντος κάθε

όζου. Τα χαρακτηριστικά αυτά συσχετίζονται με τη δομή των τόνων του γκρι αποτελούν χρήσιμη

πληροφορία για την πιθανότητα εμφάνισης κακοήθειας. Τέσσερα χαρακτηριστικά

υπολογίστηκαν από το ιστόγραμμα, 26 από τη μήτρα co-occurrence [ 73 ] και 10 από τη μήτρα

run-length [ 74 ].

2.2.2 Αξιολόγηση Επίδοσης Συστήματος Ταξινόμησης

Η επίδοση των αλγόριθμων ταξινόμησης εξετάστηκε με την μέθοδο leave-one-out. Σύμφωνα με

την leave-one-out ο ταξινομητής σχεδιάζεται με όλα τα διανύσματα του σχεδιαστικού σετ πλην

ενός. Το τελευταίο θεωρείται αγνώστου κατηγορίας και χρησιμοποιείται σαν είσοδος στον

ταξινομητή για χαρακτηρισμό. Όλη η διαδικασία επαναλαμβάνεται για όλα τα διανύσματα του

εκπαιδευτικού σετ σε συνδυασμούς των δύο, τριών, τεσσάρων σε καθολική έρευνα.

Κλασσικοί ταξινομητές: Υλοποιήθηκαν κλασσικοί ταξινομητές όπως ο ελάχιστης απόστασης

(minimum distance - MD), ελαχίστων τετραγώνων ελάχιστης απόστασης (least square minimum

distance – LSMD), Bayesian, και τεχνητών νευρωνικών δικτύων (artificial neural networks -

MLP),[72,83,84,170] των οποίων η ακρίβεια ταξινόμησης χρησιμοποιήθηκε ως αναφορά για την

αξιολόγηση της απόδοσης των σύγχρονων ταξινομητών που περιγράφονται στην συνέχεια.

XIV

Σύγχρονοι ταξινομητές: Ταξινομητής Μηχανών Διανυσμάτων Στήριξης (Support Vector

Machines-SVMs) [87,88]. Η βασική ιδέα για την εφαρμογή των SVMs για την αντιμετώπιση

προβλημάτων ταξινόμησης συνίσταται σε δύο βήματα:

1. Μετασχηματισμός των ανυσμάτων εκπαίδευσης (που στην γενική περίπτωση δεν είναι

γραμμικώς διαχωρίσιμα) σε ένα μεγαλύτερων διαστάσεων χώρο (feature space) μέσω μιας

κατάλληλης συνάρτησης (συνάρτηση πυρήνα), ώστε να καταστούν γραμμικώς διαχωρίσιμα.

2. Υπολογισμός του βέλτιστου διαχωριστικού ορίου (margin) ανάμεσα στις δύο κατηγορίες με

τέτοιο τρόπο ώστε να ικανοποιούνται οι ακόλουθες συνθήκες:

α) το εύρος του διαχωριστικού ορίου να είναι μέγιστο, και

β) το πλήθος των σημείων που βρίσκονται εντός του ορίου αυτού να είναι ελάχιστο.

Στην περίπτωση δύο κατηγοριών, η συνάρτηση διάκρισης (discriminant function) ενός

ταξινομητή βασισμένο στα SVMs είναι:

g(x) = sign ⎟⎟⎠

⎞⎜⎜⎝

⎛+∑

=

bKyN

iiii

1

),( xxα

όπου x το προς ταξινόμηση διάνυσμα, Ν το πλήθος των ανυσμάτων εκπαίδευσης, xi το i-οστό

άνυσμα εκπαίδευσης, yi ∈ -1,+1 αναλόγως την κατηγορία, αi, b συντελεστές βαρύτητας και

Κ(x,xi) η συνάρτηση πυρήνα.

Οι συναρτήσεις πυρήνα πρέπει να ικανοποιούν συγκεκριμένες συνθήκες (συνθήκες Mercer

[177]) και, ενδεικτικά, οι πλέον διαδεδομένες στη διεθνή βιβλιογραφία είναι:

Η πολυωνυμική συνάρτηση:

( )( )diT

iK 1),( += xxxx όπου d ο βαθμός του πολυωνύμου,

Η Gaussian Radial Basis συνάρτηση:

⎟⎠⎞⎜

⎝⎛= −−

2

2

2exp),(

σi

iK xxxx

όπου σ η τυπική απόκλιση.


Για τον SVM-ταξινομητή με τον πολυωνυμική συνάρτηση πυρήνα 3ου βαθμού, ο καλύτερος

συνδυασμός χαρακτηριστικών ήταν ο μέση τιμή (mean value) των τόνων του γκρι από

ιστόγραμμα και η sum variance από την μήτρα co-occurrence επιτυγχάνοντας ποσοστό επιτυχίας

96.7%. Ο καλύτερος συνδυασμός χαρακτηριστικών για όλες τις wavelet συναρτήσεις πυρήνες

ήταν παρόμοιος με αυτόν του πολυωνυμικού πυρήνα βαθμού 3 rd (μέση τιμή και sum variance).

XV

Για τον ταξινομητή MLP η υψηλότερη ακρίβεια ταξινόμησης επιτεύχθηκε από τον συνδυασμό

της μέσης τιμής και του χαρακτηριστικού Run Length Non Uniformity από τη μήτρα run-length

επιτυγχάνοντας ποσοστό επιτυχίας 95.0%. Για τους ταξινομητές (QLSMD, QB) ο καλύτερος

συνδυασμός χαρακτηριστικών ήταν η μέση τιμή από το ιστόγραμμα, η sum variance από την

μήτρα co-occurrence και η Run Length Non Uniformity μήτρα run-length επιτυγχάνοντας

ποσοστό επιτυχίας 92.5% και οι δύο (Πίνακας 3.1).

Πίνακας 2.1 Ποσοστά ταξινόμησης διαφόρων ταξινομητών για τις μεθόδους leave-one-out και

re-substitution.

Ακρίβεια Ταξινόμησης LOO+ (%) Resub.* (%) NSV**

SVM με πολυωνυμική συνάρτηση πυρήνα 1ου βαθμού 89.2 93.3 17




SVM με RBF συνάρτηση πυρήνα 94.2 97.5 15

SVM με Daubechies Wavelet συνάρτηση πυρήνα 95.8 98.3 9

SVM με Coiflet Wavelet συνάρτηση πυρήνα 97.5 100.0 10

SVM με Symmlet Wavelet συνάρτηση πυρήνα 95.0 99.2 10

MLP 95.0 96.6

QLSMD 92.5 96.7

Bayesian 92.5 95.8 + Leave-one-out Μέθοδος * Re-substitution Μέθοδος ** Αριθμός των διανυσμάτων στήριξης κατά την re-substitution μέθοδο

2.2.4 Συμπεράσματα:

Ο βέλτιστος συνδυασμός χαρακτηριστικών γνωρισμάτων του υπολογιστικού συστήματος

ανίχνευσης προτύπων (μέση τιμή και sum variance) αντιστοιχεί με τις διάφορες παραμέτρους

υφής (ηχογένεια, παρουσία αποτιτανώσεων) που αποτελούν κλινικές ενδείξεις κακοήθειας του

όζου [17,18,25,27]. Αναλυτικά, η μέση τιμή των τόνων του γκρι συσχετίζεται άμεσα με την

ηχογένεια του όζου σε σχέση με τον περιβάλλοντα ιστό, ενώ το δεύτερο χαρακτηριστικό (sum

variance) εκφράζει τις χρήσιμες χωρικές πληροφορίες και αντιστοιχεί με την παρουσία δομών

όπως διάφορες αποτιτανώσεις στο εσωτερικό του όζου. Διάφορα χαρακτηριστικά που πηγάζουν

από το ιστόγραμμα και την μήτρα co-occurrence έχουν επίσης υποδειχθεί στις προηγούμενες

ποσοτικές μελέτες [164] με απώτερο σκοπό την πρόγνωση κακοήθειας των όζων, σημειώνοντας

ακρίβειας ταξινόμησης της τάξης του 85%. Εφάμιλλες ακρίβειες (83,9%) επιτεύχθηκαν από μια

άλλη μελέτη υιοθετώντας τη συνάρτηση διαχωρισμού (discriminant function) των όζων [166]. Η

XVI

υψηλότερη ακρίβεια που επιτεύχθηκε στην παρούσα μελέτη οφειλόταν πιθανότατα στην

καλύτερη διακριτική ικανότητα του υπερηχογραφικού συστήματος καθώς και στην μη γραμμική

φύση του ιδιαίτερα περίπλοκου αλγορίθμου SVM που υιοθετήθηκε. Τελικά, ένα ικανό σύστημα

ταξινόμησης σχεδιάστηκε, βασισμένο στον αλγόριθμο SVM, για την αξιολόγηση του ποσοστού

κινδύνου κακοήθειας σε όζους του θυρεοειδή αδένα σε εικόνες υπερηχογραφίας. Αυτό το

σύστημα θα μπορούσε να είναι ένα χρήσιμο διαγνωστικό εργαλείο σαν μια δεύτερη άποψη στον

Ιατρό και μπορεί να αποβεί σημαντικό για την ορθή διαχείριση των σθενών με σκοπό την

αποφυγή άσκοπων βιοψιών.

2.3 Υπολογιστικό Σύστημα Αναγνώρισης Προτύπων βασισμένο σε

Χαρακτηριστικά Περιγράμματος και Τοπικών Μεγίστων

2.3.1 Βάση Δεδομένων

Υπερηχογραφικές εικόνες από 86 διαφορετικούς ασθενείς, οι οποίοι ανήκουν και στα δύο φύλα

συλλέχθηκαν στο χρονικό διάστημα από τον Φεβρουάριο του 2005 μέχρι τον Αύγουστο του 2006

από τον ιατρικό διαγνωστικό κέντρο EUROMEDICA, Κατεχάκη 4, Αθήνα, Ελλάδα. Το σύστημα

υπερηχογραφίας, απόκτησης εικόνων και ο Ιατρός παραμένουν οι ίδιοι με την προηγούμενη

έρευνα. 12 χαρακτηριστικά περιγράμματος υπολογίστηκαν αυτόματα από την περιοχή

ενδιαφέροντος κάθε όζου. Τα χαρακτηριστικά αυτά σχετίζονται με τη μορφολογία του

περιγράμματος των όζων και αποτελούν κλινικές ενδείξεις για την πιθανότητα ύπαρξης ή όχι

κακοήθειας σε αυτούς. Επίσης υπολογίστηκαν 8 χαρακτηριστικά βασισμένα στα τοπικά μέγιστα

από τον μετασχηματισμό μικροκυματιδίων. Θα πρέπει να αναφερθεί ότι τα χαρακτηριστικά αυτά

χωριστήκαν σε δύο κατηγορίες.. Στην μία, τα χαρακτηριστικά προέρχονται από τα τοπικά

μέγιστα που δεν αντιστοιχούν σε speckle, ενώ στην άλλη προέρχονται από το σύνολο των

τοπικών μεγίστων πριν την ανάλυση της κανονικότητας τους. Ο σκοπός είναι να διερευνηθεί η

επίδραση που έχει το speckle στην σωστή αξιολόγηση της εικόνας.

2.3.2 Αξιολόγηση Επίδοσης Συστήματος Ταξινόμησης

Η αξιολόγηση των αλγόριθμων ταξινόμησης πραγματοποιήθηκε με την ROC ανάλυση

υλοποιώντας την μέθοδο leave-one-out. Όλη η διαδικασία επαναλαμβάνεται για όλα τα

διανύσματα του εκπαιδευτικού σετ σε συνδυασμούς των δύο, τριών, τεσσάρων σε εκτεταμένη

έρευνα. Ο ταξινομητής με την μεγαλύτερη τιμή της περιοχής κάτω από την καμπύλη ROC

XVII

(AUC) για έναν συγκεκριμένο συνδυασμό χαρακτηριστικών θεωρείται ότι επέτυχε τον

μεγαλύτερη ποσοστό επιτυχίας

Σύγχρονοι ταξινομητές: Εκτός του Ταξινομητή Μηχανών Στήριξης Διανυσμάτων (Support

Vector Machines-SVMs) στην παρούσα έρευνα χρησιμοποιήθηκαν και τα Πιθανοκρατία

Νευρωνικά δίκτυα.

Πιθανοκρατία Νευρωνικά δίκτυα (Probabilistic Neural Networks-PΝΝ): Τα PNN

μοντελοποιούν τον Bayesian ταξινομητή, ο οποίος ελαχιστοποιεί το ενδεχόμενο σφάλμα

ταξινόμησης ενός προτύπου σε λάθος κατηγορία. Ενώ ο Bayesian ταξινομητής θεωρεί κανονική

την κατανομή της πιθανότητας, τα PNN εκτιμούν την συνάρτηση πυκνότητας πιθανότητας μέσω

μη παραμετρικών μεθόδων (Parzen). Τα PNN είναι feed-forward δίκτυα δομημένα σε τέσσερα

επίπεδα.

α) επίπεδο εισόδου: σε αυτό το επίπεδο υπάρχουν τόσα στοιχεία, όσα και τα πρότυπα

εκπαίδευσης

β) πρότυπο επίπεδο: αυτό το επίπεδο περιέχει κ στοιχεία, ένα για κάθε δείγμα εκπαίδευσης. Σε

κάθε κόμβο του επιπέδου υπολογίζεται η απόσταση του διανύσματος εισόδου από τα πρότυπα

εκπαίδευσης.

γ) επίπεδο άθροισης: έχει τόσα στοιχεία όσες και οι προς διαχωρισμό τάξεις και απλά προσθέτει

τις εξόδους του προηγούμενου επιπέδου

δ) επίπεδο εξόδου: τα στοιχεία εξόδου κρίνουν το αποτέλεσμα της ταξινόμησης

Το κυριότερο πλεονέκτημα των PNN έγκειται στο γεγονός ότι η εκπαίδευση είναι εύκολη και

γρήγορη και σε σχέση με άλλα είδη νευρωνικών δικτύων και ότι δεν απαιτεί ανάδραση.

Η συνάρτηση διαχωρισμού ενός PNN για j κατηγορίες δίνεται από την κάτωθι εξίσωση

[84,85,86]:

∑=

−−

=Nj

ijppj

i

eN

g1

22/

2

2

)2(1)( σ

σπ

xx

x

όπου x είναι το άνυσμα προς κατηγοριοποίηση, xi αίναι το i άνυσμα εκπαίδευσης, Nj ο αριθμός

των ανυσμάτων στην κατηγορία j, σ είναι μια παράμετρος εξομάλυνσης, και p είναι ο αριθμός

των χαρακτηριστικών. Η ταξινόμηση του εκάστοτε ανύσματος πραγματοποιείται στην κατηγορία

με την μεγαλύτερη τιμή της συνάρτησης διαχωρισμού.

2.3.2.1 Αξιολόγηση των δύο ταξινομητών χωρίς την παρουσία του speckle

Όσον αφορά τον ταξινομητή SVM, η υψηλότερη ακρίβεια ταξινόμησης με τον ελάχιστο αριθμό

χαρακτηριστικών (AUC – 0,96) επιτεύχθηκε με τον συνδυασμό των εξής χαρακτηριστικών: Την

XVIII

ομαλότητα του περιγράμματος (Smoothness) την συμμετρία του όζου (Symmetry) και την τυπική

απόκλιση των τοπικών μεγίστων, χρησιμοποιώντας την πολυωνυμική συνάρτηση πυρήνα 2ου

βαθμού. Ο ταξινομητής PNN επέτυχε την υψηλότερη ακρίβεια ταξινόμησης (AUC – 0.91) με τον

εξής συνδυασμό χαρακτηριστικών "fractal dimension, την παρουσία κοιλοτήτων (Concavity) και

την τυπική απόκλιση των τοπικών μεγίστων " (Πίνακας 2.2).

Πίνακας 2.2 Αποτελέσματα ανάλυσης ROC για τους ταξινομητές SVM και PNN για τους

αντίστοιχους καλύτερους συνδυασμούς χαρακτηριστικών

Model AUC (Lower – Upper 95.0%

Confidence Limit)

Sensitivity (SN)

Specificity (SP)

Likelihood Ratio

SN/(1-SP)

Number of

Support Vectors

SVM με πολυωνυμική συνάρτηση πυρήνα 1ου

βαθμού

0.88 (0.69 – 0.96) 0.93 0.90 9.3 13


βαθμού

0.96 (0.84 – 0.99) 0.93 0.98 46.5 7


βαθμού

0.92 (0.78 – 0.97) 0.87 0.93 12.4 10


βαθμού

0.89 (0.69 – 0.97 ) 0.93 0.93 13.3 12

SVM με RBF συνάρτηση πυρήνα

0.91 (0.79 – 0.96) 0.93 0.96 23.2 17

PNN 0.91 (0.85 – 0.95) 0.96 0.94 16

2.3.2.2 Αξιολόγηση των δύο ταξινομητών με την παρουσία του speckle

Ο ταξινομητής SVM επέτυχε την υψηλότερη ακρίβεια ταξινόμησης χρησιμοποιώντας τον

πολυωνυμικό πυρήνα 3ου βαθμού (AUC – 0.88) με τη μέθοδο leave-one-out χρησιμοποιώντας το

συνδυασμό χαρακτηριστικών "τυπική απόκλισης των ακτινών του περιγράμματος και της

συμμετρίας του όζου (Symmetry)".

Ο ταξινομητής PNN σημείωσε την υψηλότερη ακρίβεια ταξινόμησης (AUC – 0.86) υιοθετώντας

τον εξής: συνδυασμό χαρακτηριστικών γνωρισμάτων: Η εντροπία των ακτινών του

περιγράμματος και η παρουσία των κοιλοτήτων (concavity) (Πίνακας 2.3).

XIX

Πίνακας 2.3 Αποτελέσματα ανάλυσης ROC για τους ταξινομητές SVM και PNN για τους

αντίστοιχους καλύτερους συνδυασμούς χαρακτηριστικών


Confidence Limit)

Sensitivity (SN)

Specificity (SP)

Likelihood Ratio

SN/(1-SP)

Number of Support Vectors


βαθμού

0,83 (0,63 – 0,93) 0.74 0.90 7.4 11


βαθμού

0,86 (0,68 – 0,94) 0.74 0.91 8.3 11


βαθμού

0,88 (0,68 – 0,97) 0.93 0.96 23.2 10


βαθμού

0,78 (0,52 – 0,86) 0.70 0.85 4.6 13

SVM με RBF συνάρτηση πυρήνα

0,79 (0,66 – 0,91) 0.74 0.87 5.6 13


βαθμού

0,86 (0,74 – 0,90) 0.84 0.88 7


Σχετικά με την έρευνα χωρίς την παρουσία του speckle, και οι δύο ταξινομητές SVM και PNN

αξιοποίησαν την περίπλοκη σχέση μεταξύ της μορφής των όζων και των χαρακτηριστικών που

προέρχονται από τα τοπικά μέγιστα προς μια ακριβή διαφοροποίηση μεταξύ των όζων χαμηλού

και υψηλού κινδύνου. Η παρουσία μικρών κοίλων περιοχών (concativity) και η αυξανόμενη

ανομοιομορφία (ομαλότητα) στο περίγραμμα των όζων από κοινού με την αξιοπρόσεχτη διαφορά

μεταξύ του πλάτους και του μήκους της (συμμετρία) και την αυξανόμενη μεταβλητότητα των

αποτιτανώσεων (MCs) έχουν αποδειχθεί ως σημαντικά και λεπτομερή χαρακτηριστικά που

οδηγούν προς την υποψία καρκίνου.

Αντίθετα, η έλλειψη κοίλων σημείων, η ύπαρξη μιας ομαλής οριογραμμής, ένα σχεδόν

στρογγυλό σχήμα των όζων μαζί με την παρουσία αποτιτανώσεων χωρίς διαφορά στον τόνο του

γκρι αποτελούν χαρακτηριστικά τα οποία τείνουν να αθωώσουν τον όζο.

Σχετικά με την έρευνα με την παρουσία του speckle, Ο αντίκτυπος που είχε στη διαδικασία

επιλογής των χαρακτηριστικών προς το βέλτιστο συνδυασμό με το υψηλότερο ποσοστό

ακρίβειας ήταν μεγαλύτερος από τον αναμενόμενο στην αρχή αυτής της μελέτης. Η συνολική

ακρίβεια και των δύο ταξινομητών παραμένει σχετικά υψηλή (AUCSVM – 0.88, AUCPNN – 0.86),

εντούτοις η χρησιμοποίηση των χαρακτηριστικών που προέρχονται μόνο από τη μορφολογική

ομάδα είναι ένα ζήτημα που απαιτεί την περαιτέρω έρευνα. Η μείωση του αριθμού

XX

χαρακτηριστικών γνωρισμάτων χωρίς την σημαντική μείωση της συνολικής ακρίβειας μπορεί να

θεωρηθεί ως σημαντικό προτέρημα στην πολυπλοκότητα αλγορίθμων όπως οι SVM και PNN.

Παρόλα αυτά, δεν μπορεί να αντισταθμίσει τη διαγραφή των σημαντικών πληροφοριών

(παρουσία αποτιτανώσεων ή όχι, συνάθροιση αυτών ή όχι, κ.λ.π...) που παρέχουν τα

χαρακτηριστικά που προέρχονται από τα τοπικά μέγιστα.

Σαν τελικό συμπέρασμα μπορεί να ειπωθεί ότι, το συνεχώς αυξανόμενο ποσοστό πληροφοριών,

που προέρχεται από την εικόνα υπερήχου, έχει μετατρέψει την απόφαση για το κατά πόσον θα

πρέπει να υποβληθεί σε βιοψία ένας ασθενής, σε μια μάλλον σύνθετη διαδικασία. Αυτό το

γεγονός καθιστά τους αλγορίθμους αναγνώρισης προτύπων ως ουσιαστικό βοηθητικό εργαλείο,

προκειμένου να παραμετροποιηθούν και να ποσοτικοποιηθούν όλες οι διαθέσιμες πληροφορίες.

- 1 -

CHAPTER 1

Introduction

1.1 Power of Ultrasound

The establishment of Ultrasonography (US) as a leading tool in the majority of medical

applications worldwide, is directly associated with the evolution of imaging technology employed

in medicine and biology. The design and implementation of novel and -state of the art- ultrasound

systems, allowed US to infiltrate into medical applications such as Orthopedics, I.C.U,

Diabetology etc, in which few years ago the performing of US examinations was prohibited. The

latter modified the use of prognostic medicine nowadays in a radical way. In fact,

ultrasonography is recognized as the fundamental technique in prevention, diagnosis and therapy

of a constantly broadened spectrum of diseases. US imposes itself on the hands of every

physician anywhere he practices medicine. From a small private clinic via a portable unit to a

general hospital through an expensive four-dimensional system, ultrasound proves its efficiency

and accuracy in a daily basis.

1.2 Need for Image Processing and Analysis Methods in Thyroid Ultrasound Images

Despite its non-invasive nature, low cost and easy-to-use real time application, US imaging

suffers from the presence of a granular pattern termed as speckle. It is the result of various

constructive and destructive interference phenomena, which occur when the distances between

the tissue scatterers are smaller than the axial resolution limit of the system. It causes deformities

of anatomic structures as well as random fluctuations in the image’s intensity profile. If an image

is corrupted with speckle there are no regions of approximately constant intensity profile even if

the reflecting tissue is entirely uniform. In addition, several US properties can lead to misleading

effects in the ultrasound image. Reverberation, shadowing, refraction, side and grating lobes

deteriorate the resolution of the US image, thus degrade its overall quality. The aforementioned

problems arising by the complex nature of US imaging constitute speckle suppression and

accurate boundary detection as important steps towards US image quality and diagnostic

procedure enhancement in medical ultrasound imaging.

The sonographic evaluation of malignancy risk in thyroid nodules represents a typical example of

the way ultrasonography is accomplished to gain the confidence of medical community

throughout the past years. The medical interest regarding biopsy’s necessity based on sonographic

Introduction

- 2 -

criteria is extremely high. New and more detailed features that have derived from US

examinations of thyroid nodules are investigated to decide whether to proceed or not into Fine

Needle Aspiration Biopsy (FNAB). Features, such as the nodule’s echo-structure and

echogenicity (solid or colloid, hyper-hypo or iso-echogenic), its shape differentiation (round, egg-

shape, wide or tall), its boundary irregularity degree (from normal to highly irregular borderline),

its calcifications pattern (massive, snow-storm etc), are employed towards an improved

prognosis. The increasingly amount of information provided by high resolution US systems

constitutes the clinical decision procedure rather difficult, therefore the quantification of

sonographic findings and the implementation of computer-based algorithms could be of

assistance as a second opinion tool.

1.3 Aims, Contributions and Novelties of Thesis

The aim of the present thesis was the design and implementation of new image processing and

analysis methods in ultrasound thyroid images. The research procedure comprised two main

concepts towards optimization of thyroid ultrasonography. The design and implementation of:

1. Wavelet-based image processing methods towards speckle suppression and thyroid nodule

segmentation

2. Image analysis methods in order to evaluate the thyroid nodules malignancy risk factor.

1.3.1 Wavelet–Based Image Processing

Most contemporary vision algorithms cannot efficiently perform on image intensity values that

are directly derived from the initial gray-level representation. These intensity values are highly

redundant, while the amount of important information within the image may be small. The

depiction of ultrasound intensity values under a different angle of view can reveal several

significant features that are not easily distinguishable in the original image. The wavelet-based

transformation from the initial ultrasound image representation into a feature representation

explicitly reveals the useful image features without the loss of essential image information,

reduces the redundancy of the image data and eliminates any irrelevant information [55].

When an image contains meaningful structures of various sizes, the scale parameter should vary.

Edges at different scales correspond to different physical entities. Large objects are well

represented in large scale whereas small structures are localized in small scales. The multi-

resolution wavelet analysis provides information content of images by viewing any sharp

variations (edges) at different scales by investigating the neighbors of these edges with the

neighboring size varying [57,58].

Chapter 1

- 3 -

Since edges are considered as efficient descriptors of images, the multi-resolution formalism has

the ability to detect and record them towards edge detection and segmentation purposes. Wavelet

theory offers a mathematical framework for the multiscale processing and relates the behavior of

edges across scales to local image properties. Mallat and Zong [62] have proved that a multiscale

edge representation can provide a complete and stable representation of a signal, which in turn

means that the whole signal information is carried by those multiscale edges. The latter denotes

that image processing methods can be preferably utilized on the edge representation than directly

onto the intensity value representation. Isolated edges or contours (group of edges with similar

properties) correspond to sharp contrasts and can be detected from the local maxima of the

wavelet transform. The multiscale local maxima representation is a reorganization of image

information that provides higher level description of structures.

A remarkable property of the wavelet transform is its ability to characterize the local regularity of

image features such as discontinuities and sharp cusps. In mathematics, this local regularity is

often measured with Lipschitz exponents [61]. The multiscale edge representation provides the

ability to detect all the singularities (small points in space of sudden localized changes, which

often indicate the most important features) of an image and to measure their Lipschitz regularity.

In this thesis, an investigation has been made to the local behavior of image singularities in terms

of Lipschitz regularity in thyroid ultrasound images. The wavelet transform modulus maxima

created by noise singularities have a different behavior than those that are mainly affected by

image singularities. The following realization has been made; the additive signal dependent noise

random field, obtained by the speckle model implemented in this thesis, is a distribution which is

almost everywhere singular or discontinuous, with non-positive Lipschitz exponents. On the

contrary, the worth singularities derived from non irregular texture are sharp cusps that have

positive Lipschitz exponents.

As an application, an algorithm has been developed that removes speckle noise from ultrasound

images by analyzing the evolution of wavelet transform modulus maxima across scales. This

inter-scale search has been implemented by zooming into edges, beginning at low resolution

(large scales) and adaptively increasing the resolution (small scales) to acquire the necessary

details. In the resulting de-speckled ultrasound image, contrast enhancement of various structures

in regard with the surrounding environment without the creation of blurring has been observed. In

addition, according two independent observers the disclosure of structures that are not easily

distinguishable by the human eye has also been reported.

The two-microlocalization properties [69] of these edges that provide characterization of

singularities have also been utilized in the subsequent segmentation algorithm. The multiscale

Introduction

- 4 -

information acquired by the aforementioned study has been integrated towards the nodule

boundary detection. A multi-scale hybrid model has been introduced that employed wavelet local

maxima, after the regularity estimation, towards object identification in order to extract the

thyroid nodule’s boundary. The proposed model transfers the multiscale local maxima

representation into a multiscale object representation. Each object that occupies a physical region

has been detected by means of local maxima adjacency in all available scales. The multiscale

structure representation associates an anatomical object in the image with a volume in the multi-

scale edge transform. This structure representation serves as input to a constrained Hough

transform for nodule detection. The segmentation method offered an additional tool in the shape-

based thyroid nodule categorization from the physician and accuracy enhancement during fine

needle aspiration procedure.

1.3.2 Image Analysis

Finally, an investigation of various pattern recognition methods for automatic thyroid nodule

discrimination in terms of high and low risk of malignancy has been made. Various pattern

recognition algorithms such as Support Vectors Machines (SVMs), the Probabilistic Neural

Network (PNN), the classical quadratic least squares minimum distance (QLSMD), the quadratic

Bayesian (QB) and the multilayer perceptron (MLP) classifiers, have been implemented

throughout this thesis. This research comprised two independent studies that employed initially

textural features and subsequently morphological and wavelet based features derived from the

segmentation procedure.

The texture-based classification scheme implemented in this study has managed to quantify

several textural parameters visually evaluated by physicians in assessing the thyroid nodule’s risk

factor and succeeded high classification rates. These parameters mainly involved echogenicity in

regard with the surrounding environment, presence of calcifications within the nodule and

increased vascularity.

An additional study has also been made that aimed at the employment of quantified

morphological and wavelet-based features, in order to evaluate the malignancy risk factor in

ultrasound thyroid nodules. In this research, a novel approach has been made that utilized the

image singularities in order to evaluate the effect of speckle in the classification procedure. In a

parallel study (with and without speckle), the pattern recognition algorithms employed various

wavelet features so as to evaluate the discrimination importance of speckle. As a conclusion,

speckle noise, even if in the original US image its effect cannot be easily evaluated; in the

wavelet feature level its presence had a negative influence.

Chapter 1

- 5 -

The quantification of various sonographic observations (such as echogenicity, the boundary

irregularity degree, the non-circular boundary and the presence of micro-calcifications) led to a

more objective evaluation towards biopsy necessity and could be of assistance in the decision

making procedure.

1.4 Publications

The research work of this thesis has resulted or contributed in publications and presentations in

international journals and conferences.

1.4.1. Publications in peer reviewed international journals

Journal Published Papers:

1. S. Tsantis, D. Cavouras, I. Kalatzis, N. Piliouras, N. Dimitropoulos, and G. Nikiforidis:

Development of a support vector machine-based image analysis system for assessing the

thyroid nodule malignancy risk on ultrasound, Ultrasound in Medicine and Biology, Vol. 31,

No. 11, pp. 1451–1459, 2005

2. S. Tsantis, N. Dimitropoulos, D. Cavouras and G. Nikiforidis: A Hybrid Multi-Scale Model

for Thyroid Nodule boundary detection on Ultrasound Images, Computer Methods and

Programs in Biomedicine, Volume 84, Issues 2-3, Pages 86-98, 2006

3. S. Tsantis, N. Dimitropoulos, M. Ioannidou, D. Cavouras and G. Nikiforidis: Inter-Scale

Wavelet Analysis for Speckle Reduction in Thyroid Ultrasound Images, Computerized

Medical Imaging and Graphics, Volume 31, Issue 3, Pages 117-127, 2007

Journal Submitted Papers:

4. S. Tsantis, N. Dimitropoulos, D. Cavouras, and G. Nikiforidis: Pattern Recognition Methods

Employing Morphological and Wavelet Local Maxima Features towards Evaluation of

Thyroid Nodules Malignancy Risk in Ultrasonography, Submitted in Ultrasound in Medicine

and Biology, April 2007.

1.4.2. Publications in International Conference Proceedings

1. S. Tsantis, N.Dimitropoulos, D. Cavouras and G. Nikiforidis: Morphological Features

towards Ultrasound Thyroid Nodules Malignancy Evaluation, 2nd IC-EpsMsO, Athens, 4-7

July, 2007

2. S. Tsantis, N.Dimitropoulos, D. Cavouras and G. Nikiforidis: 1st Order vs. 2nd Order

Derivatives towards Wavelet-Based Speckle Suppression in Ultrasound Images, 2nd IC-

EpsMsO, Athens, 4-7 July, 2007

Introduction

- 6 -

3. S. Tsantis, D. Gklotsos, I. Kalantzis, N. Piliouras, P. Spyridonos, N.Dimitropoulos, G.

Nikiforidis and D. Cavouras: Computer Assisted Diagnosis of Thyroid Nodules Malignancy

Risk.. European Congress of Radiology, 2005

4. S. Tsantis, I.Kalantzis, N Piliouras, D. Cabouras, N Dimitropoulos, G. Nikiforidis: Computer-

aided characterization of thyroid nodules by image analysis methods, Proceedings in

International Conference of Computational Methods in Sciences and Engineering 2003

(ICCMSE 2003), pp 639:642, September 2003

5. S. Tsantis, D. Cabouras, N Dimitropoulos, G. Nikiforidis: Denoising sonographic images of

thyroid nodules via singularity detection employing the wavelet transform modulus maxima,

Proceedings in International Conference of Computational Methods in Sciences and

Engineering 2003 (ICCMSE 2003), pp 643:646, September 2003.

6. S. Tsantis, N.Piliouras, N.Dimitropoulos, D. Cavouras and G.Nikiforidis: Evaluation of

Support Vector Machines Wavelet kernels for the automatic categorization of thyroid

nodules, 4th European Symposium on Biomedical Engineering, Patra, 25th - 27th June 2004

7. Stavros Tsantis, Dimitris Glotsos, Giannis Kalatzis, Nikos Dimitropoulos, George

Nikiforidis, Dionisis Cavouras: Automatic contour delineation of thyroid nodules in

ultrasound images employing the wavelet transform modulus-maxima chains, 1st International

Conference “From Scientific Computing to Computational Engineering”, IC-SCCE, Athens,

8-10 September, 2004

8. Stavros Tsantis, Dimitris Glotsos, Panagiota Spyridonos, Giannis Kalatzis, Nikos

Dimitropoulos, George Nikiforidis, Dionisis Cavouras: Improving Diagnostic Accuracy in

the classification of thyroid cancer by combining quantitative information extracted from

both ultrasound and cytological images, 1st International Conference “From Scientific

Computing to Computational Engineering”, IC-SCCE, Athens, 8-10 September, 2004

1.4.3. Contributions in Publications in International Conference Proceedings

1. Glotsos D., Spyridonos P., Tsantis S., Kalatzis I., Dimitropoulos N., Nikiforidis G., Cavouras

D: Unsupervised Segmentation of Fine Needle Aspiration Nuclei Images of Thyroid Cancer

using a Support Vector Machine Clustering Methodology, 1st International Conference “From

Scientific Computing to Computational Engineering”, IC-SCCE, Athens, 8-10 September,

2004

Chapter 1

- 7 -

2. D. Glotsos, S. Tsantis, J. Kybic 12, I. Kalatzis, P. Ravazoula, N. Dimitropoulos, G.

Nikiforidis, D. Cavouras, ‘Pattern recognition based segmentation versus wavelet maxima

chain edge representation for nuclei detection in microscopy images of thyroid nodules’, 3rd

European Medical and Biological Engineering Conference, Prague, Czech Republic, 20-25

November, 2005.

3. Glotsos D., Spyridonos P., Ravazoula I., Kalatzis I., Tsantis S., Nikiforidis G., Cavouras D:

Evaluating the Generalization Performance of a Support Vector Machine based Classification

Methodology in Brain Tumor Astrocytomas Grading, 1st International Conference “From

Scientific Computing to Computational Engineering”, IC-SCCE, Athens, 8-10 September,

2004.

4. Contribution in Dimitris Glotsos and Jan Kybic: Development of a wavelet-assisted edge-

detection algorithm for boundary detection of fine needle aspiration images of thyroid

nodules. Research Report CTU-CMP-2005-17, Center for Machine Perception, K13133 FEE

Czech Technical University, Prague, Czech Republic, March 2005

1.5 Dissertation Layout

In Chapter 2, a background on thyroid physiology and anatomy is provided as well as the grading

categories of solitary thyroid nodules. In Chapter 3, a theoretical background on physics and

instrumentation of ultrasound in general is presented. Moreover, the quality control procedure and

the data acquisition system employed in this thesis are also given. Chapter 4 provides an

overview of classic wavelet theory and wavelet transforms. Emphasis is given to redundant

dyadic wavelet transform since it is the basis of the wavelet-based techniques used in this thesis.

In Chapter 5 the regularity theory along with its correlation to wavelet transform modulus

maxima is depicted. Chapter 6 describes the fundamentals of pattern recognition theory and

various classification algorithms with a thorough study in feature selection and generation

methods. In Chapter 7, a survey of various speckle suppression methods in ultrasonography is

presented first. Then, a new wavelet-based method for speckle reduction in thyroid ultrasound

imaging is explained in detail. Chapter 8 contains at first an extensive review of various

segmentation algorithms in ultrasound imaging. Consequently a novel hybrid model is presented

towards boundary extraction of thyroid nodules in ultrasound. In Chapter 9, an SVM model is

designed and implemented in order to assess thyroid nodule malignancy risk factor that employed

several textural characteristics of the sonographic image. Chapter 10 encloses a pattern

recognition study based on two well known classification algorithms (SVMs and PNN) that

Introduction

- 8 -

employed morphological in conjunction with various wavelet local maxima features directly

derived from the segmentation procedure. In Chapter 11, a general conclusion and some future

perspectives of the present thesis are provided. In Appendixes I, II, III, IV the List of Figures, List

of Tables, Abbreviations and Index of this manuscript are listed respectively.

1.6 Research Funding

The present research was funded by the Operational Program for Educational and Vocational Training

II (EPEAEK II).

- 9 -

CHAPTER 2

Thyroid Gland

2.1 Introduction

The thyroid gland is a brownish-red and highly vascular organ, located in the front of the

lower neck and attached between the lower part of the larynx and the upper part of the

trachea. The gland varies from an H to a U shape formed by two elongated lateral lobes. Both

lobes are about 4 cm long and 1-2 cm wide and are linked together by a median isthmus [1]

(Figure 2.1).

Figure 2.1 The thyroid gland.

The thyroid gland produces, stores and secrets thyroid hormones, which are peptides

containing iodine. The two most important hormones are tetraiodothyronine (thyroxine or T4)

and triiodothyronine (T3). They are essential for humans and have many effects on body

metabolism, growth, and development. The thyroid gland’s function is influenced by

hormones produced by two organs:

1. The pituitary gland, located at the base of the brain which produces thyroid stimulating

hormone (TSH) and,

2. The hypothalamus, a small part of the brain above the pituitary that produces

thyrotropin releasing hormone (TRH) (Figure 2.2).

Low levels of thyroid hormones in the blood are detected by the hypothalamus and the

pituitary. TRH is released, stimulating the pituitary to release TSH. Increased levels of TSH,

in turn, stimulate the thyroid to produce more thyroid hormone, thereby returning the level of

thyroid hormone in the blood back to normal. The three glands and the hormones produce the

"Hypothalamic - Pituitary - Thyroid axis". Once thyroid hormone levels are restored, TSH

secretion stabilizes at a high level. [2-4].

Thyroid Gland

- 10 -

Figure 2.2 Schematic representation of Hypothalamic - Pituitary - Thyroid axis

2.2 Thyroid Disorders

The enlargement of the thyroid gland is called goitre. Goitre does not always indicate a

disease, since thyroid enlargement can also be caused by physiological conditions such as

puberty and pregnancy [5,6]. The main causes of thyroid disease are:

1. Excessive thyroid hormone production or hyperthyroidism.

2. Decreased thyroid hormone production or hypothyroidism.

3. The state of normal thyroid function is called euthyroidism.

All thyroid disorders are much more common in women than in men. Other disorders termed

as "Autoimmune" of the thyroid gland are also common. These are caused by abnormal

proteins, (called antibodies), and the white blood cells which act together to stimulate or

damage the thyroid gland. Graves' disease (hyperthyroidism) and Hashimoto's thyroiditis, are

diseases of this type [7-12].

Graves' Disease: Graves' disease (thyrotoxicosis) is due to a unique antibody called "thyroid

stimulating antibody" which stimulates the thyroid cells to grow larger and to produce

excessive amounts of thyroid hormones. In this disease, the goitre is due not to TSH but to

this antibody.

Hashimoto's Thyroiditis: In Hashimoto's thyroiditis, the goitre is caused by an accumulation

of white blood cells and fluid (inflammation) in the thyroid gland. This leads to destruction of

the thyroid cells and, eventually, thyroid failure (hypothyroidism). As the gland is destroyed,

thyroid hormone production decreases; as a result, TSH increases, making the goitre even

larger. Hyperthyroidism is treated mostly by medical means, but occasionally it may require

the surgical removal of the thyroid gland.

Sometimes, thyroid enlargement is restricted to one part of the gland. The most common

cause of this is a cyst or nodule, which may be benign or malignant. Occasionally there are

many nodules. This, so called "multinodular goitre", is probably caused by mutations of

follicular cells. Thyroid nodules are not expression of a single disease but constitute the

Chapter 2

- 11 -

clinical indication of a wide range of different diseases. An initial differentiation within

thyroid nodules subjects to quantitative criteria. A single nodule is called solitary nodule

whereas the presence of multiple nodules is often called as multinodular goitre. Although as

many as 50% of the population will have a nodule somewhere in their thyroid, the vast

majority of these are benign. Occasionally, solitary thyroid nodules can take on characteristics

of malignancy and require either a needle biopsy or surgical excision.

2.3 Management of solitary nodules

The parameters that must be considered into a clinical decision, regarding solitary nodules,

include the history of the lesion, age, sex, and family history of the patient, physical

characteristics of the gland, local symptoms, and laboratory evaluation. The age of the patient

is an important consideration since the ratio of malignant to benign nodules is higher in youth

and lower in older age. Male sex also carries a similar importance.

The basics steps towards an efficient management of solitary nodules include [13-16]:

• Clinical examination

• Thyroid function tests: TSH, antibodies…

• Ultrasound

• Τhyroid scan

• Cytology of fine needle aspirate (FNA)

Clinical examination: The physician inspects the neck and feels the thyroid gland

(palpation). The size and consistency of the thyroid gland, how painful it is, and the extent to

which it may have moved out of position from surrounding structures are also assessed by the

physician.

Thyroid function tests: Through a blood test the thyroid gland’s functionality can be

evaluated. Measurements of T3, T4 and hormones that control thyroid gland activity (the TSH

test) are taken and compared with the norm.

Ultrasound: High-resolution ultrasonography (US) can be used to determine the size and

presence of nonpalpable nodules as small as 1 mm within the thyroid tissue (Figure 2.3).

Furthermore, any solid or cystic components within a thyroid nodule can be detected with

high precision [17-27].

In this examination technique, different types of body tissue conduct and reflect sound in

different ways. The reflecting echo is recorded and displayed as an image from the part of the

body from which it resonated. Ultrasound has now established itself as a standard means of

examination in thyroid gland morphology. In cases where a nodule presents some suspicious

US characteristics, a fine needle aspirate biopsy (FNAB) is performed. In a review of

published studies, the use of conventional thyroid ultrasonography did not allow accurate

prediction between malignant and benign cases of solitary thyroid nodules. Its main

Thyroid Gland

- 12 -

indications are accurate measurement of size and as a guide for FNAB. However, certain US

features such as irregular borders of the nodule, lack of a "halo", echogenicity, evidence of

calcium flakes, marginal nodules in a cyst, increased blood flow, and growth on consecutive

ultrasounds, are suggestive signs of malignancy.

Figure 2.3 Ultrasonographic examination in the transverse plane of the thyroid containing a

solid nodule in the right lobe and a homogeneous appearance on the left lobe.

Thyroid scan: By using thyroid gland scintigraphy, a morphological and functional image of

the thyroid gland is produced simultaneously. This means that the way different areas of the

thyroid gland are depicted relates to how they are functioning (normally, hyperactively or

hypoactively). Such examinations were obligatory before, with the use of radio-iodine for

treating thyroid gland disorders [28,29]. Thyroid scan can differentiate a solitary nodule as

cold (Hypo-functioning) nodule or hot (Hyper-functioning) nodule (Figure 2.4).

(a) (b)

Figure 2.4 Scintiscans of thyroid. (a)The scan on the left is normal. (b) A typical scan of a

"cold" thyroid nodule failing to accumulate iodide isotope is shown on the right.

The thyroid scan can also provide evidence for a diagnosis in a multinodular goiter, in

Hashimoto’s thyroiditis, and rarely in thyroid cancer when functioning cervical metastases are

seen. Malignant tumors usually fail to accumulate iodide to a degree equal to that of the

normal gland.

Chapter 2

- 13 -

FNAB: Fine needle aspiration biopsy has become the diagnostic tool of choice for the initial

evaluation of solitary thyroid nodule because of its accuracy, safety, and cost effectiveness. In

most –but not all– cases, FNAB is the only non-surgical method which can differentiate

malignant and benign nodules [30,31]. Fewer patients have undergone thyroidectomy for

benign disease as a result of FNAB, with resultant decreased health care costs. Although

needle biopsy can be performed easily, consistently obtaining adequate tissue and processing

the specimens to achieve accurate cytopathological interpretation, requires expertise and

experience. The needle is placed into the nodule several times and cells are aspirated into a

syringe. The cells are placed on a microscope slide, stained, and examined by a pathologist.

Often a small percentage of FNA’s are termed as Nondiagnostic, which indicate that there are

an insufficient number of thyroid cells in the aspirate and no diagnosis is possible. A

nondiagnostic aspirate should be repeated.

2.4 Grading

Various alternative classifications of thyroid nodules have been proposed. A summarized

classification approach based on cytology findings is illustrated in Figure 2.5 [32,33].

Follicular Cells(hyperplasia)

Thyroid Nodules

Benign Nodules Malignant Nodules

Anaplastic Carcinoma

Lymphoma

Papillary Carcinoma

Medullary Carcinoma

Focal Hemorrhage

Inflammatory

Simple Cyst

non-functioning follicularadenoma

Colloid Cyst

Follicular carcinoma

Indeterminate

Figure 2.5 Classification of thyroid solitary nodules

Bening nodules: The great majority of solitary thyroid nodules are benign (>90%). Common

types of the benign thyroid nodules are simple thyroid cysts, inflammatory cysts and cysts

with focal haemorrhage [34].

Thyroid Gland

- 14 -

Adenomatous Hyperplasia: An interesting fact regarding bening nodules, is that a certain

category (epithelial hyperplastic nodules) can, under particular circumstances, be transformed

into malignant ones. The thyroid cells on these aspirates are neither clearly benign nor

malignant [45,46]. Twenty five percent of such suspicious lesions are found to be malignant

when these patients undergo thyroid surgery. These are usually follicular cell cancers (Figure

2.6). Therefore, surgery is recommended for the treatment of thyroid nodules from which a

suspicious aspiration has been obtained.

(a) (b)

Figure 2.6 (a) Thyroid nodule with epithelial hyperplasia, (b) Colloid nodule.

Malignant nodules: Most thyroid cancers are very curable. In fact, the most common types

of thyroid cancer (papillary and follicular) are the most curable. In younger patients, both

papillary and follicular cancers can be expected to have better than 97% cure rate if treated

appropriately. Both papillary and follicular cancers are typically treated with complete

removal of the lobe of the thyroid which harbors the cancer [35-38]. Medullary cancer of the

thyroid is significantly less common, but has a worse prognosis. Medullary cancers tend to

spread to large numbers of lymph nodes very early on therefore requiring a much more

aggressive operation than does the more localized cancers such as papillary and follicular.

The least common type of thyroid cancer is anaplastic which has a very poor prognosis [39-

40].Most primary thyroid lymphomas occur in middle-aged or elderly patients with a ratio of

women-men ranging from 2:1 to 8:1. Patients present with a relatively rapid thyroid

enlargement accompanied by hoarseness, dysphagia and/or dyspnea in approximately 25% of

cases and cord paralysis in about 17% [41-43]. Anaplastic thyroid cancer tends to be found

after it has spread and is not cured in most cases. Often an operation cannot remove the entire

tumor [44]. One of the objectives of this thesis is to explore all available ultrasonic

characteristics by means of image analysis methods in order to predict the malignancy risk

factor between high risk nodules (adenomatus or epithelial hyperplasia) and low risk nodules

(simple or colloid cysts).

- 15 -

CHAPTER 3

Physics & Instrumentation of ultrasound

3.1 Nature of Ultrasound

A sound or ultrasound (US) wave consists of a mechanical disturbance of a medium (gas,

liquid or solid) which passes through the medium at a fixed speed. The rate at which particles

in the medium vibrate is the frequency of the sound and is measured in hertz (cycles/second).

In medical ultrasound, the disturbance which is characterized by the local pressure change of

the particles of the medium from the resting positions originates at a piezoelectric transducer

in a probe placed on the skin surface. The transducer (operating as a transmitter) transforms

electrical signals to mechanical movement. The same transducer can transform the reflecting

mechanical vibrations into electrical signals (operating as a receiver). The ultrasound

frequencies used in contemporary US systems range from 1 to 20 MHz [47,48].

3.2 Propagation in Tissue

Ultrasound is altered by the tissue through which it passes. At the boundaries between

different tissue types, the US beam can be partially reflected, refracted, scattered by small

tissue structures or subjected to energy loss by absorption [49,50].

Reflection: When ultrasound is incident on a smooth boundary (interface) between two media

some ultrasound is transmitted through the interface and some reflected. If the interface is

perpendicular to the direction of propagation the intensity of the reflected ultrasound beam is

proportional to the acoustic impedances of the two media.

Refraction: The transmitted beam at an interface between media having different speeds of

ultrasound deviates from the path of incident beam, provided the angle of incident is non-

zero. The beam deviation is dependent on the difference of ultrasound speed (not impedances)

and the refracted beam bends away from the perpendicular if the speed in the second medium

is higher than in the first and vice versa.

Scattering: If ultrasound is incident on a rough surface or on particles with size small or

comparable with the beam’s wavelength then the ultrasound is scattered in all directions. If

the scattering particles are small compared with the wavelength then the scattered power is

proportional to the fourth power of the ultrasound frequency.

Absorption: Ultrasound power is also subjected to absorption in which the energy of the

ultrasound is converted into heat. The loss due to absorption increases with frequency.

Physics & Instrumentation of Ultrasound

- 16 -

3.3 Pulse – Echo Imaging

At a boundary between two tissues a proportion of ultrasound passes on and the rest is

reflected. The degree of reflection depends on the acoustic impedances of the two tissues

which are depended on density and compressibility. A large difference in acoustic impedance

(i.e. soft tissue – bone or soft tissue – air interfaces) leads to a high degree of reflection. At the

boundary between two different types of soft tissue (i.e. muscle – fat) the degree of reflection

is small [51].

In ultrasonic imaging the transducer is periodically driven by an electrical pulse leading to the

transmission of an ultrasound pulse which is received back after reflection or scattering at

tissue interfaces. The time of arrival of the echo from a given interface depends on its depth

and the US system employs the time of echo’s arrival after the transmission as an indication

of the depth of the interface. Since the amplitude of an echo is determined by the structure and

physical decomposition of the reflector or scatterer, it is used to determine the brightness of

the echo in a display.

B – Mode: In this imaging technique the ultrasound beam is scanned through the tissue. The

echo signals received at each beam position are displayed as spots on the monitor screen in

which the brightness indicate the echo amplitude (grayscale display). The positions of the

spots are determined by the orientation of the beam and by the time of arrival of the echoes.

M – Mode: The movement of echo-generating tissues can be displayed as a function of time

by means of the M-mode display.

Doppler Mode: Movement of reflectors or scatterers also changes the frequency of the

received signal. This change from the transmitted signal frequency is known as the Doppler

Effect and the magnitude of the change (Doppler shift) is proportional to the reflector or

scatterer velocity. By measuring the Doppler shift, the cyclical variation of blood velocity can

be monitored. The integration of real time Doppler instruments produces a color-flow image

which is superimposed in the grayscale display.

3.4 Instrumentation

All US examinations throughout this thesis were performed on an HDI-3000(Figure 3.1) ATL

digital ultrasound system – Philips Ultrasound P.O. Box 3003 Bothel, WA 98041-3003, USA

– with a wide band (5-12 MHz) linear probe (L7-4) using various scanning methods such as

longitudinal and transversal cross sections of the thyroid gland. The system is located in

Medical Imaging Department, EUROMEDICA Medical Center, 2 Mesogeion Avenue,

Athens, Greece.

Chapter 3

- 17 -

Figure 3.1 HDI-3000-ATL digital ultrasound system

The wide-band linear ultrasound transducer has the capacity to resonate at multiple

frequencies which in turn gives the system the ability to acquire a wide range of frequencies

(5-9 MHz), contrary to conventional transducers that detects only the nominal frequency (7

MHz), producing US images of high quality (Figure 3.2).

Figure 3.2 US image of the thyroid gland with a cystic nodule.

3.5 Quality Control of the Ultrasound System

Before the acquisition and storage of US image in the computer a thorough quality control is

performed on the system. The quality control procedure utilized a tissue mimicking phantom

– RMI 403 LE, GAMMEX RMI P.O. Box 620327 Middleton, WI 53562-0327 USA – with

the same attenuation and speed of sound as human soft tissue with uniform scatter distribution


- 18 -

that yields a smooth image texture. The image quality indicators employed in the procedure

are presented below:

Depth of Penetration: The point at which usable tissue information disappears – or

maximum depth of penetration is reached – can be defined simply as how far one can “see”

into the phantom. Equipment sensitivity and noise determines the deepest echo signal which

can be detected and clearly displayed.

Image Uniformity: Ultrasound systems can produce various image artefacts and non-

uniformities which in some cases mask variations in tissue texture. Common non-uniformities

are horizontal bands in the image caused by inadequate handling of transitions between focal

zones or vertical bands indicating inactive or damaged transducer elements.

Axial Resolution: Axial resolution describes the scanner’s ability to detect and clearly

display closely spaced objects that lie on the beam’s axis. Using pin targets of decreased

vertical spacing, the system’s axial resolution is determined by locating the two resolvable

pins with the smallest separation.

Distance Accuracy: Vertical and horizontal distance measurement errors can easily go

unnoticed on clinical images. Distance accuracy as a quality indicator is determined by

comparing the measured distance between selected pin targets in the phantom with the known

distance.

Lateral Resolution: Lateral resolution is described as the distinction of small adjacent

structures perpendicular to the beam’s major axis. The lateral resolution is measured

indirectly by measuring the width of pin targets at depths corresponding to near, mid, and far

field ranges of the transducer.

Dead Zone: The dead or “ring down” zone is the portion of the image directly under the

transducer where image detail is missing or distorted. The depth of an instrument’s dead zone

is determined by identifying the shallowest pin target that can be clearly visualized.

All steps carried out during the quality control procedure were upon the guidelines

determined both from the ultrasound system and Phantom manufacturer user manuals and the

performance of the system was accordingly to the standard specifications.

3.6 Data Acquisition and Storage

An image processing system for acquisition and storage of US images consists of the US

system, a personal computer and an interface between the system and the computer (Figure

3.3). The interface converts analog information into digital data which the computer can

process. This takes place in a special piece of hardware, the frame grabber, which also stores

the image. Usually the frame grabber package contains a library of often-used routines which

can be linked to the user’s program.

Chapter 3

- 19 -

The frame grabber utilized in the present study is the Miro – PCTV (Pinnacle Systems Inc.

280 N.Bernardo Avenue Mountain View, CA 94043) with the BT 848 chipset integrated. The

video output of the ultrasound system (HDI 3000) is connected to the frame grabber of the

image processing computer (Microsoft PC, PII at 600 MHz with 64 MB of RAM).

Figure 3.3 Image processing system for acquisition and storage of US images.

The BT848 chipset integrates an NTSC/PAL/SECAM composite, an S-Video decoder, a

scaler, a DMA controller, and a PCI Bus master on a single device. It can place video data

directly into host memory for video capture applications and into a target video display frame

buffer for video overlay applications. BT848 is designed to efficiently utilize the available

132 MB/s PCI bus. The video stream consumes bus bandwidth with average data rates set to

44 MB/s for full size 768x576 PAL RGB32.

Consecutive video frames can be written into the Video image buffer (continuous capture

mode). The external trigger (Freeze command) signal temporarily stops this process thus

freezing the video. When the external trigger is disabled the video buffer is then again written

to, by every consecutive frame until the software through the radiologist issues another

FREEZE command. The selected US Images are captured at frame rate (40 ms, 25 Hz - PAL

standard video signal) and converted into JPEG format images with a resolution of 768x576


- 20 -

(full PAL resolution) pixels. The software of acquisition and storage of US images is the

Icon-Print 2000, it is written in Visual C ++ and uses technology VFW (Video for Windows).

- 21 -

CHAPTER 4

The Wavelet Transform

Summary

This chapter reviews the theory behind wavelets and wavelet transforms. At first a small

review of the continuous wavelet transform is given, followed by an extensive study of the

dyadic wavelet transform both in one dimensional (1-D) signals and two dimensional (2-D)

images. The 2-D redundant dyadic wavelet transform is implemented and utilized throughout

this thesis. Special reference is made also to the spline wavelets employed in this thesis.

Moreover, a summary is given regarding the advantages of the redundant dyadic wavelet

transform. The multi-scale edge representation is also analyzed and depicted at the last part of

this chapter.

4.1 Wavelet Theory

Wavelets are an extension of windowed Fourier analysis by Gabor [52], in which through a

fixed window a large number of oscillations are used for detecting high frequencies, whereas

a small number is used to detect low frequencies. However, in the first case the window is

‘blind’ to smooth events and in the second case the window probably will miss a brief change.

Instead of a fixed window and a variable number of oscillations Morlet and Grossman [53]

employed a ‘mother wavelet’ which is stretched or compressed to change the size of the

window, thus providing a decomposition of the signal at different scales (frequency bands).

The dilation of the function called ‘mother wavelet’ produces a family of functions. The

wavelet transform of a signal is a sequence of signals obtained by the convolution of the

signal with the wavelet family. The wavelets size variation due to dilation permits them to

automatically adapt to the different components of the signal. A small window (high

frequency band) detects rapid high-frequency components and a large window (low frequency

band) traces slow low-frequency components. The wavelet transform is required to satisfy a

so called admissibility condition so that it can form a complete and numerically stable

representation. The wavelet transform gives a representation that has good localization in both

frequency and space [54-56]. The localization in frequency implies a correspondence between

a scale of the wavelet transform and a frequency band. The overall study across all available

frequency bands is called multiresolution analysis [57-59]. The wavelet transform is divided

in two main categories: the continuous wavelet transform (CWT) in which all values of the


- 22 -

parameters are employed and the discrete wavelet transform (DWT) in which only a discrete

set of parameters are considered.

4.2 Continuous Wavelet Transform

The continuous wavelet transform is shift invariant thus suitable for feature extraction and

image analysis methods [62]. The CWT decomposes a signal by means of dilated and

translated wavelets. Let a wavelet )()( 2 ℜ∈ Lxψ is a function of zero average:

0)( =∫∞

∞−dxxψ 4.1

It is normalized 1=ψ and centered in the neighborhood of x = 0. The function ψ(x) is used

to create a wavelet family by dilating ψ with s:

⎟⎠⎞

⎜⎝⎛=

sx

sxs ψψ 1)( 4.2

All the functions in the wavelet family have the same shape as the wavelet. The continuous

wavelet transform of a signal )(2 ℜ∈ Lf is a family of functions [ ] +∈Rss xfW )( and defined

by:

+∈∗= RsxfxfW ss ),()( ψ 4.3

If )(ˆ ωψ is the Fourier transform of ψ(x), then:

)()(ˆ)(ˆ ωωψω fsfWs = 4.4

In order for the transform to be invertible, the wavelet ψ(x) must satisfy the admissibility

condition [53]:

∫∞+

∞−+∞<=

ωωωψψ

dC 2)(ˆ 4.5

The function f(x) can be reconstructed from its wavelet transform [53]:

∫∞+− ∗=

0

1 )(ˆ)(:s

dsxfWxfW ssψ 4.6

The admissibility condition also ensures that the wavelet transform is an isometry:

Chapter 4

- 23 -

∫∞+

=0

22 )()(s

dsxfWxf s 4.7

Equation 4.7 implies that the continuous wavelet transform is a complete and numerical stable

representation.

4.3 Redundant Dyadic Wavelet Transform (1-D)

In the translation-invariant dyadic wavelet transform the scale parameter s is discretized

dyadically ( Zjj][2 ∈ ) to simplify the numerical calculations, while the spatial parameter is

continuous [60,61]. Let a wavelet )()( 2 ℜ∈ Lxψ is a wavelet whose average is zero. The

wavelet family by dilating ψ with s is:

)2

(21)(2 jj

xxj ψψ = 4.8

The dyadic wavelet transform of a function f(x)∈L2, at a given scale j2 and at the position x

obtained by the convolution of f(x) with the wavelet family

)()(22

xfxfW jj ψ∗= 4.9

We refer to the dyadic wavelet transform as the sequence of functions:

ZjxfWWf j ∈= ))((2

, 4.10

where W is the dyadic wavelet transform operator.

In order to study the completeness and stability of the DWT we denote the Fourier transform

of )(2

xfW j as:

)2(ˆ)(ˆ)(ˆ2

ωψωω jffW j = 4.11

Given that there are two strictly positive constants A & B such that:

BARZj

j ≤≤∈∀ ∑∈

2)2(ˆ, ωψω , 4.12

it is ensured that the whole frequency axis is covered by dilations of )(ˆ ωψ by Zjj

∈)2( so that

)(ˆ ωf and consequently )(xf can be recovered from its dyadic wavelet transform. The

reconstructing wavelet )(xχ is any function whose Fourier transform satisfies:


- 24 -

∑+∞

−∞=

=j

jj .1)2(ˆ)2(ˆ ωχωψ 4.13

If equation (4.12) is valid, an infinite number of functions )(ˆ xχ exist that satisfy equation

(4.13). The inverse dyadic wavelet transform that recovers )(xf is given by the summation:

∑+∞

−∞=

∗=j

jj fWxf ).()( 22 χχ 4.14

In practice, we can compute a Wavelet Transform only over finitely many scales. This is

because the observed data is limited between a non-zero small (fine) scale and a finite large

(coarse) scale. According to Mallat [57], one can normalize the observable finest scale to

1(20) and the coarsest scale to 2J where J is dependent on the sample size of the data. In order

to model this scale limitation, a real function φ(x) is introduced, whose Fourier transform is an

aggregation of )2(ˆ ωψ j and )2(ˆ ωχ j at scales j2 larger than 1:

∑+∞

=

=1

2)2(ˆ)2(ˆ)(ˆ

j

jj ωχωψωφ 4.15

The reconstructive wavelet )(ωχ is such a function that )(ˆ)(ˆ ωχωψ is a positive, real and

even function. The equation (4.13) implies that the integral of )(xφ is equal to 1 and hence

that it is a smoothing function. Let jS2

be the smoothing operator defined by:

)()(22

xfxfS jj φ∗= , )2

(21)(

2 jjxxj φφ = 4.16

If the scale j2 is larger, the more details of f(x) are removed by jS2

. For any scale 2J>1

equation (4.15) yields:

∑=

=−J

j

jjJ

1

22)2(ˆ)2(ˆ)2(ˆ)(ˆ ωχωψωφωφ 4.17

From this equation it is derived that the higher frequencies of )(1 xfS , which have

disappeared in )(2

xfS J can be recovered from the dyadic wavelet transform JjfW j ≤≤12 ][

between the scale j2 and 2J.

In numerical applications, the input signal is measured at a finite resolution and thus the

wavelet transform cannot be computed at any arbitrary scale. The original signal can be

Chapter 4

- 25 -

considered as a discrete sequence ZnndD ∈= ][ of finite energy. If two constants C1>0 and

C2>0 exist, such that )(ˆ ωφ satisfies:

22)(1,2

CnCRn

≤+≤∈∀ ∑+∞

−∞=

πωφω 4.18

From Equation 4.18 the periodic signal D can be considered as the sampling of a smoothed

version of )()( 2 ℜ∈ Lxf at the finest scale 1:

ndnfSZn =∈∀ )(, 1 4.19

The input signal can thus be rewritten as ZnnfSD ∈= )]([ 1 . Mallat and Zhong [62] have

proposed the redundant discrete wavelet transform (RDWT), utilizing a particular class of

wavelets, to compute a uniform sampling of the wavelet transform of f(x) at any scale larger

than 1.

Let us denote [ ]Zn

d wnfSfS Jj ∈+= )(22 and Zn

d wnfWfW jj ∈+= )]([ 22 where w is a

sampling shift that depends on ψ(x). For any coarse scale 2J the sequence of discrete signals:

Jjdd fWfS jJ ≤≤122

][, 4.20

is called the discrete dyadic wavelet transform of ZnnfSD ∈= )]([ 1 . The coefficient signal

][ 2 fW dj provide the details of the input signal at scales Jj ≤≤1 and the coarse signal

fS dJ2

provides the approximation of the input signal at the coarse scale 2J. The filter bank

algorithm for computing 1-D RDWT is presented in Figure 4.1. The left size shows the

decomposition into wavelet coefficients and the right the reconstruction from wavelet

coefficients.

G(ω)

Η(ω)

Η(2ω)

G(2ω)

Η(4ω)

G(4ω)

Η*(4ω)

Κ(4ω)

Η*(2ω)

Κ(2ω)

Κ(ω)

Η*(ω)

f(x)=S1f(x) f(x)

W1 f(x)

W2 f(x)

W3 f(x)

S2 f(x)

S3 f(x)

+

+

+

Figure 4.1 One-dimensional – three level – redundant discrete dyadic wavelet transform.


- 26 -

The algorithm does not involve sub-sampling and is similar to the ‘algorithme ά trous’

(algorithm with holes) [63], which also does not involve sub-sampling. Filters H(ω), G(ω)

and K(ω), are 2π periodic and satisfy the perfect reconstruction condition:

1)()()( 2 =+ ωωω KGH 4.21

At dyadic scale j, the discrete filters H j, G j, K j, are obtained by inserting 22-1 zeros between

each of the coefficients of the corresponding filters at scale 21. The scaling (smoothing)

function φ(x) defined in equation (4.15) can be derived from H(ω) using the equation:

∏+∞

=

−− Η=1

)2()(ˆρ

ρωωωφ iwe 4.22

where the sampling shift parameter w is adjusted so that φ(x) is symmetrical with respect to 0.

Equation (4.22) implies that

)(ˆ)()2(ˆ ωφωωφ ωHe iw−= 4.23

A wavelet ψ(x) is defined, whose Fourier transform )(ˆ ωψ is given from the equation:

)(ˆ)()2(ˆ ωφωωψ ωGe iw−= 4.24

The reconstruction wavelet χ(x) is derived from the equation:

)(ˆ)()2(ˆ ωφωωχ ωΚ= iwe 4.25

A class of filters that satisfy equation (4.21) has been provided by Mallat and Zhong [62].

H(ω) was chosen to obtain a wavelet ψ(x) which is anti-symmetrical, as regular as possible

and has a compact support. The wavelet ψ(x) is also equal to the first order derivative

(gradient) of a smoothing function θ(x):

dxxdx )()( θψ = 4.26

Filters H(ω), G(ω) and K(ω) are given by:

122/ ))2/(cos()( += νω ωω ieH 4.27

)2/sin(4)( 2/ ωω ωieG = 4.28

Chapter 4

- 27 -

)()(1

)(2

ωω

ωGH

K−

= 4.29

All filters have compact support and are either symmetrical or anti-symmetrical. From

equations (4.22 & 4.24) the corresponding scaling and wavelet functions can be derived as:

12

2/)2/sin()(ˆ

+

⎟⎠⎞

⎜⎝⎛=

n

ωωωφ 4.30

22

4/)4/sin()(ˆ

+

⎟⎠⎞

⎜⎝⎛=

n

iωωωωψ 4.31

The Fourier transform of the smoothing function θ(x) is therefore:

22

4/)4/sin()(ˆ

+

⎟⎠⎞

⎜⎝⎛=

n

ωωωθ 4.32

We have chosen 2n+1=3. In order to have a wavelet anti-symmetrical with respect to 0 and

φ(x) symmetrical with respect to 0, the shifting constant w is equal to ½. From equations (4.31

& 4.32) it can be proven that ψ(x) is a quadratic spline wavelet with compact support, while

θ(x) is a Gaussian-like cubic spline whose integral is equal to 1. These functions are depicted

in Figure 4.2.

(a) (b)

Figure 4.2 (a) A cubic spline function and (b) a wavelet that is a quadratic spline of compact

support.

Mallat [64] have extended this class of filters and derived wavelet functions ψ(x) that are

equal to the second order derivative (Laplacian) of a smoothing function.

2

2 )()(dx

xdx θψ = 4.33


- 28 -

4.4 Redundant Dyadic Wavelet Transform (2-D)

Let )2

,2

(21),( 11

2 jjjyxyxj ψψ = and )

2,

2(

21),( 22

2 jjj

yxyxj ψψ = . The dyadic wavelet

transform of a 2-D function )(),( 22 RLyxf ∈ has two components defined by:

Zj

yxfWyxfWWf jj ∈= ),(),,( 2

212

4.34

where the Fourier transforms of ),(12 yxfW j and ),(2

2 yxfW j are given respectively by:

)2,2(ˆ),(ˆ),(ˆ)2,2(ˆ),(ˆ),(ˆ

222

112

yj

xj

yxyx

yj

xj

yxyx

ffW

ffW

j

j

ωωψωωωω

ωωψωωωω

=

= 4.35

and )2,2(ˆ 1y

jx

j ωωψ , )2,2(ˆ 2y

jx

j ωωψ are the Fourier transforms of the partial wavelet

functions ),(),,( 21 yxyx ψψ respectively. The function f(x,y) can be reconstructed from its

dyadic wavelet function with:

( )∑+∞

−∞=

∗+∗=j

yxWyxWyxf jjjj ),(),(),( 22

22

12

12

χχ 4.36

where the partial reconstruction wavelets ),(12 yxjχ and ),(2

2 yxjχ satisfy the equation:

( )∑+∞

−∞=

=+j

yj

xj

yj

xj

yj

xj

yj

xj 1)2,2(ˆ)2,2(ˆ)2,2(ˆ)2,2(ˆ 2211 ωωχωωψωωχωωψ 4.37

The scaling function is an aggregation of )2(ˆ ωψ j and )2(ˆ ωχ j at scale 2j greater than 1:

( )∑+∞

=

=+=1

221121)2,2(ˆ)2,2(ˆ)2,2(ˆ)2,2(ˆ),(ˆ

jy

jx

jy

jx

jy

jx

jy

jx

jyx ωωχωωψωωχωωψωωφ 4.38

The approximation of f(x) at scale j2 is defined as a convolution with a dilated scaling

function )(2

xjφ :

),(),(22

yxfyxfS jj φ∗= 4.39

In practice, the input image is measured in finite resolution and thus the wavelet transform

cannot be computed at any arbitrary fine scale. Similarly to the 1-D case, if the discrete signal

has a finite number N x Ν pixels, it is symmetrically extended to 2N x 2Ν pixels. The discrete

Chapter 4

- 29 -

periodic image D can then be considered as the sampling of a smoothed version of a function

f(x,y) at the finest scale 1:

,, 2Zmn ∈∀ mndmnfS ,1 ),( = 4.40

The 2-D RDWT of Mallat and Zhong [62], computes the uniform sampling of the wavelet

transform of f(x,y) at any larger scale than 1, using a particular class of wavelets. For any

coarse scale j2 , the RDWT is defined as a sequence of discrete coefficients:

Jjd

Jjdd fWfWfS jjj ≤≤≤≤ 1

,221

,122

,, 4.41

where

( )( )

( )),(

,),(

),(

22

22

,22

12

,12

wmwnfSfS

wmwnfWfW

wmwnfWfW

jj

jj

jj

d

d

d

++=

++=

++=

4.42

and w is a sampling shift that depends on the choice of wavelets. The coefficient images

fW dj,1

2and fW d

j,2

2, provide the details of the input image at scales Jj ≤≤1 and the coarse

image fS j2 provides the approximation of the input image at the coarse scale 2J. The filter

bank algorithm for computing the 2-D RDWT is depicted in Figure 4.3.

G(ωy)

Η(ωx)Η(ωy)

Η(2ω)

G(2ωx)

G(4ωx)

Η*(4ωx)Η*(4ωy)

Η*(2ω)

Κ(ωy)L(ωx)

Η*(ωx)Η*(ωy)

f(x,y)=S1 f f(x,y)W2

1 f

W31

f

S2 f

S3 f

+

+

+

G(ωx) Κ(ωx)L(ωy)W1

1 f

W12

f

G(2ωy) Κ(2ωy)L(2ωx)W2

2 f

Κ(2ωx)L(2ωy)

Η(2ωx)Η(2ωy)

G(4ωy)

W32

f

Η(4ωx)Η(4ωy)

Κ(4ωx)L(4ωy)

Η*(2ωx)Η*(2ωy)Κ(4ωy)L(4ωx)

Figure 4.3 Two dimensional – three level – redundant dyadic wavelet transform.


- 30 -

The left side depicts the decomposition into wavelet coefficients, and the right the

reconstruction from wavelet coefficients. Filters H(ω), G(ω), K(ω) and L(ω) are 2π periodic

and satisfy the perfect reconstruction condition:

2)(1

)(

1)()()(2

2

ωω

ωωω

HL

KGH

+=

=+ 4.43

At dyadic scale j, the discrete filters H j, G j, K j, L j and are obtained by inserting 22-1 zeros

between each of the coefficients of the corresponding filters at scale 21. The 2-D wavelets are

given by expressions analogous to that of the 1-D case. The class of spline functions

described in the previous section is used. The wavelets are partial derivatives of 2-D

smoothing functions:

xyxyx

∂∂

=),(),(

11 θψ and

xyxyx

∂∂

=),(),(

22 θψ 4.44

where the functions ),(1 yxθ and ),(2 yxθ are numerically closed to a single smoothing

function ),( yxθ .

The redundant wavelet representation presented in this section has several advantages with

respect to orthogonal wavelet representation. The sub-band images are shift invariant [65], do

not present aliasing and have the same number of pixels as the original, thus the

representation is highly redundant. Moreover, smooth symmetrical or anti-symmetrical

wavelet functions can be used, allowing the alleviation of any boundary effects via mirror

extension of the signal. Due to these advantages it has been extensively used for denoising,

segmenting and pattern recognition applications. An example of the RDWT employed in the

Circle image is depicted in Figure 4.4.

Chapter 4

- 31 -

fS1

fS J2

fW 121

fW 221

fW 122

fW 222

fW 123

fW 223

fW 124

fW 224

Figure 4.4 Redundant dyadic wavelet transform of the Circle image.


- 32 -

4.5 Multiscale Edge Representation (MER)

Gradient Vector: Let ),( yxθ be a symmetrical smoothing function approximating the

Gaussian. As already explained in details in the precious section the RDWT of a function

)(),( 22 RLyxf ∈ is the set of functions )),(),,(( 22

12

yxfWyxfW jj , which are respectively

the partial derivative along the horizontal and vertical orientation of the convolution

of ),( yxf by the smoothing function ),( yxθ , dilated along a dyadic sequence Ζ∈jj )2( and is

given by [62]:

( )( )

( )( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∗∂∂

∗∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛∗=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

yxfy

yxfxf

yxfWyxfW

j

j

j

j

j

j j

,

,2

),(),(

2

2

22

12

2

1

2

2

θ

θ

ψψ

4.45

where ),(1 yxψ and ),(2 yxψ are the analyzing wavelets and j the dyadic scale.

Equation 4.45 indicates that the above set of functions can be viewed as the two components

of the gradient vector of ),( yxf smoothed by ),( yxθ at each scale j2 :

),)(*(2),(),(

22

1

2

2 yxfyxfWyxfW

j

j

j j θ→

∇⋅=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ 4.46

The modulus – angle representation of the gradient vector is given by:

22

222

12

),(),(),( yxfWyxfWyxfM jjj += 4.47

and

),(),(

arctan),( 22

12

2 yxfWyxfW

yxfAj

j

j = 4.48

Modulus Maxima: The sharper variation points of ),(*2

yf j χθ at a scale j2 correspond to

edges, are obtained from the local maxima of ),(2

yxfM j along the gradient direction given

by ),(2

yxfA j . The gradient direction values ),(2

yxfA j were constricted to the following

values [66]:

⎭⎬⎫

⎩⎨⎧

47,

23,

45,,

43,

2,

4,0 πππππππ

At each scale j2 of the Dyadic Wavelet Transform, the point (x,y) where the modulus of the

Chapter 4

- 33 -

gradient vector ),(2

yxfM j is maximum compared with its neighbor’s locally positioned in

the direction specified by ),(2

yxfA j , is called modulus maxima (Figure 4.5). Each time

such a point is detected, the position of the resultant local maxima is recorded as well together

with the values of the modulus ),(2

yxfM j and angle ),(2

yxfA j at the corresponding

locations [67].

),(2

yxfM j ),(2

yxfA j Local Maxima

21

22

23

24

Figure 4.5 The gradient magnitude, the gradient directions and the local maxima of the Circle

image.


- 34 -

In order to construct curves in the image plane individual wavelet modulus maxima are

connected in a certain scale if they are neighbors and the vector that joins these two points is

perpendicular to the angle direction at these points.

- 35 -

CHAPTER 5

Singularity Detection

Summary

This chapter discusses at first the theory of singularities along with their classifications

according to Lipschitz criteria. In the second part of the chapter a thorough review is given

regarding the correlation between singularity detection and wavelet transform modulus

maxima accompanied with suitable depictions.

5.1 Singularity and Mathematical Description

Singularities are points of sharp variations, which often indicate the most important features

of the estimated functions. A specific singularity called change-point, which describes sudden

localized change, is of important interest in statistics and has been studied over years. Wavelet

analysis is an ideal tool to study localized changes such as discontinuities and sharp cusps in a

noisy function. The magnitudes and positions of singularities can be observed from the

empirical wavelet coefficients. The modulus maxima of discrete wavelet transform are

directly related to the Lipschitz regularity, a mathematical measurement of singularity [68].

The local regularity of a signal is measured with the Lipschitz criteria. Lipschitz exponents

(also called Holder exponents) provide uniform regularity measurements over time intervals,

but also at any point ν. If f has a singularity at ν, then the Lipschitz exponent at ν characterizes

this singular behavior.

Pointwise Lipschitz Regularity: A function f is pointwise Lipschitz a≥0 at v, if there exist

K>0 and a Taylor polynomial pv of degree ⎣ ⎦am = such that:

atKtptfRt νν −≤−∈∀ )()(, 5.1

A function f is uniformly Lipschitz α over [a,b] if it satisfies condition (5.1) for all ],[ bav∈ ,

with a constant K that is independent of ν. If f is uniformly Lipschitz α>m in the

neighborhood of ν, then one can verify that f is necessarily m times continuously

differentiable in this neighborhood.

If 10 <≤ a then )()( νν ftp = and the condition (5.1) becomes

atKftfRt νν −≤−∈∀ )()(, 5.2


- 36 -

A function that is bounded but discontinuous at ν is Lipschitz 0 at ν. If the Lipschitz regularity

is α<1 at ν, then f is not differentiable at ν and α characterizes the singularity type.

5.2 Wavelet Transform and Singularity

A remarkable property of the wavelet transform is its ability to characterize the local

regularity of functions. If the wavelet has n vanishing moments then we show that the wavelet

transform can be interpreted as a multiscale differential operator of order n. This yields a first

relation between the differentiability of f and its wavelet transform decay at fine scales. The

following proposition proves that a wavelet with n vanishing moments can be written as the

nth order derivative of a function θ [69]. The resulting wavelet transform is a multiscale

differential operator. We suppose that ψ has a fast decay which means that for any decay

exponent Nm∈ there is a Cm such that:

mm

tCtRt+

≤∈∀1

)(,ψ 5.3

Theorem 1: A wavelet ψ with a fast decay has n vanishing moments if and only if there is a

function θ with a fast decay such that:

n

nn

dttdt )()1()( θψ −= 5.4

As a consequence the following equation is obtained:

))((),( ufdudssuWf sn

nn θ∗= , 5.5

with: )(1)(st

sts −= θθ .

Moreover, ψ has no more vanishing moments if and only if ∫+∞

∞−≠ 0)( dttθ . The decay of the

wavelet transform amplitude across scales is related to the uniform and pointwise Lipschitz

regularity of the signal. Measuring this asymptotic decay is equivalent to zooming into signal

structures with a scale that goes to zero. Mallat [68,70] also proved that the uniform Lipschitz

regularity of f on an interval is related to the amplitude of its wavelet transform at fine scales.

Theorem 2: If RLf 2∈ is uniform Lipschitz n≤α over ],[ ba then there exists A>0 such

that:

,],[),( Rbasu ×∈∀ 2/1),( +≤ aAssuWf 5.6

Chapter 5

- 37 -

Conversely, if ),( suWf satisfies condition (5.6) and if α<n is not an integer then f is

uniformly Lipschitz α on ],[ εε −+ ba for any ε>0. Condition (5.6) signifies that the wavelet

transform ),( suWf decays like 2/1+as over intervals where f is uniformly Lipschitz α, when

the scale s goes to 0.

Theorem 3: A necessary and sufficient condition on the wavelet transform for estimating the

Lipschitz regularity of f at a point v is [69]:

,),( +×∈∀ RRsu ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+≤ +

aa

suAssuWf ν1),( 2/1 5.7

Conversely, if α<n is not an integer and there exists a constant A, and α’<α such that:

,),( +×∈∀ RRsu ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+≤ +

'2/1 1),(

aa

suAssuWf ν

5.8

then f is Lipschitz α at ν.

To interpret more easily the necessary and the sufficient conditions (5.7 & 5.8), it is supposed

that ψ has compact support equal to [-C , C]. The cone of influence of ν in the scale-space

plane is the set of points (u,s) such that ν is included in the support of )(1)(, sut

stsu

−= ψψ .

Since the support of )(s

ut −ψ is equal to [u-Cs , u+Cs], the cone of influence of ν is defined

by:

Csu ≤−ν 5.9

Theorems 2 and 3 prove that the local Lipschitz regularity of f at ν depends on the decay at

fine scales of ),( suWf in the neighborhood of ν. The decay of ),( suWf can be controlled

from its local maxima values. We use the term modulus maximum to describe any point

),( oo su such that ),( osuWf is locally maximum at u=uo. This implies that:

.0),(=

∂∂

usuWf oo 5.10

This local maximum should be a strict local maximum in either the right or the left

neighborhood of uo, to avoid having any local maxima when ),( osuWf is constant. We call

maxima line any connected curve s(u) in the scale-space plane (u,s) along which all point are


- 38 -

local maxima. In Figure (5.1) high amplitude wavelet coefficients are in the cone of influence

of each singularity.

(a)

(b)

(c)

(d)

(e)

Figure 5.1 (a),(b),(c),(d) Wavelet transform of f(t) calculated with quadratic spline wavelet

ψ=-θ’ where θ is the cubic spline smoothing function approximating the Gaussian. The red

stars are the local maxima of the wavelet coefficients along each scale. The scale increases

from top to bottom. (e) Maxima line in the scale-space plane inside the cone of influence.

5.3 Singularity Detection (1-D)

The singularities are detected by finding the abscissa where the wavelet modulus maxima

converge at fine scales. If the wavelet has only one vanishing moment, wavelet modulus

maxima are the maxima of the first order derivative of f smoothed by sθ . Hwang and Mallat

[71] proved that if ),( suWf has no modulus maxima at fine scales then f is locally regular.

Chapter 5

- 39 -

Theorem 4: Suppose that ψ is Cn with a compact support, and ψ=(-1)nθ(n) with

∫+∞

∞−≠ .0)( dttθ Let ],[1 baLf ∈ . If there exists so>0 such that ),( suWf has no local

maximum for ],[ bau∈ and s<so then f is uniformly Lipschitz n on ],[ εε −+ ba for any

ε>0.

This Theorem implies that f can be singular (not Lipschitz 1) at a point ν only if there is a

sequence of wavelet maxima points Nnnn su ∈),( that converges towards ν at fine scales:

ν=+∞→ nn

ulim and 0lim =+∞→ nn

s 5.11

These modulus maxima may or may not be along the same maxima line. The result

guarantees that all singularities are detected by following the wavelet transform modulus

maxima at fine scales. Figure (5.2) gives an example where all singularities are located by

following the maxima lines.

For a ψ=(-1)nθ(n) where θ is a Gaussian the modulus maxima of ),( suWf of any RLf 2∈

belong to connected curves that are never interrupted when the scale decreases. The decay of

),( suWf in the neighborhood of ν is controlled by the decay of modulus maxima in the cone

Csu ≤−ν [70,71]. According to Theorem 1 a function f is uniformly Lipschitz α in the

neighborhood of ν if and only if there exists A>0 such that each modulus maximum (u,s) in

the cone Csu ≤−ν satisfies:

2/1),( +≤ aAssuWf 5.12

which is equivalent to:

)(log)21(log),(log 222 saAsuWf ++≤ 5.13

Therefore, the Lipschitz regularity at ν is the maximum slope of ),(log2 suWf as a function

of log2s along the maxima lines converging to ν (Figure 5.3).


- 40 -

Figure 5.2 Wavelet transform of f(t) calculated with quadratic spline wavelet ψ=-θ’ where θ

is the cubic spline smoothing function approximating the Gaussian. The red stars are the local

maxima of the wavelet coefficients along each scale. The scale increases from top to bottom.

Chapter 5

- 41 -

Figure 5.3 The full line gives the decay of ),(log2 suWf from Figure (5.2) as a function of

log2s along the maxima line that converges to the abscissa t=11. The dashed line gives

),(log2 suWf along the maxima line that converges at t=168.

The last graph (Figure 5.3) depicts the maxima lines in the scale-space plane towards zero s

for singularity detection.

5.4 Singularity Detection (2-D)

Theorems 2 and 3 constitute an efficient proof that the wavelet transform is particularly well

adapted to estimate the local regularity of functions. The decay of the two-dimensional

wavelet transform depends on the regularity of f. We restrict the analysis to Lipschitz

exponents 10 <≤ a . A function f is said to be Lipschitz α at (xo,yo) if there exists K>0 such

that for all 2),( Ryx ∈

2/22 )(),(),( aoooo yyxxKyxfyxf −+−≤− 5.14

If there exists K>0 such that condition (5.14) is satisfied for any Ω∈),( oo yx then f is

uniformly Lipschitz α over Ω. Τhe Lipschitz regularity of a function f(x,y) is related to the

asymptotic decay at fine scales of wavelet transform along horizontal and vertical directions

|W1f(u,v,2j)| and |W2f(u,v,2j)| in the corresponding neighborhood. This decay is controlled by

it’s local maximum value Mf(u,v,2j). Like in Theorem 2 one can prove that f is uniformly

Lipschitz α inside a bounded domain of R2 is and only if there exists A>0 such that for all

(u,v) inside this domain and all scales 2 j:

)1(2)2,,( +≤ aj j

AvuMf 5.15


- 42 -

Suppose that the image has an isolated edge curve along which f has Lipschitz regularity α.

The value of )2,,( jvuMf in a two dimensional neighborhood of the edge curve can be

bounded by the wavelet modulus values along the edge curve. The Lipschitz regularity of the

edge is measured with condition (5.15) by estimating the decay exponent of the modulus

amplitude across scales.

- 43 -

CHAPTER 6

Pattern Recognition

Summary

This chapter discusses pattern recognition theory along with the implementation of various

classifiers employed in this thesis. In the first part of the chapter a detailed explanation is given

regarding the feature generation employed as input in the classification system. In the second part

the classification algorithms implemented in this thesis are presented.

6.1 Pattern Recognition Theory

Pattern recognition classifies objects into a number of categories or classes. This classification

procedure is a two-folded process which at first generates a description of the object (i.e., the

pattern) and then classifies it based on that description (i.e., the recognition). The object

description involves feature generation techniques in order to produce certain attributes, whereas

the classification task associates a predefined label with the object based on those attributes. The

main goal of each pattern recognition system is to determine the most accurate label for each

object analyzed.

The pattern recognition procedure is accomplished with a training phase that configures the

algorithms used in both the description and classification tasks based on a number of objects

whose labels are known as the training set. During the training phase, a training set is analyzed to

determine the attributes used to label the objects with the highest possible accuracy. Following

the training phase, the classification takes place to an unlabeled object based on the attributes of

that object. High coincidence between the known labels and those assigned by the pattern

recognition system denotes high classification accuracy. The methodology for description and

classification with known attributes is called supervised learning. In cases where the training set

is not available the procedure employed is termed as unsupervised learning. A common step in

the pattern recognition procedure that usually precedes the hierarchy presented before is the

isolation of the object to be recognized from the surrounding environment. This step is

prerequisite in order for the feature extraction to take place.

Pattern Recognition

- 44 -

6.2 Object Isolation

Thyroid nodules play a key role in US thyroid imaging diagnostic procedure. Thus it is very

important to extract them from the noisy environment for further processing. This isolation

procedure is termed as segmentation and a detailed review regarding the segmentation approach

employed in this thesis is presented in chapter 8.

6.3 Feature Generation

The feature generation stage is the process of computing features from an image or from a region

within this image to be used in the classification task. The generated features must encode this

kind of information in order to enhance the classification accuracy. In US thyroid nodule image

analysis, the computed features should exhibit high separability attributes between high and low

risk cases. In the current project three categories of features were employed to assess the

malignancy risk factor of thyroid nodules: (a) Textural features, (b) Shape and Geometrical

features and (c) Wavelet Local Maxima features.

6.4 Textural Features

The textural information extracted from the thyroid nodule can be employed as criteria in

assessing the risk factor of malignancy and can be of value in patient management, i.e. whether to

recommend or not surgical operation. Textural features are divided in two main categories: First

and second order statistical features.

6.4.1 First Order Statistical Features

The 1st order statistical features determine the distribution of grey level values within the thyroid

nodule [72]. The most important features are:

1. Mean value(m) N

jig

m ji∑∑

=

),(

6.1

where g(i,j) is the grey level value in the position (i,j) and N the number of pixels.

2. Standard Deviation (std) N

mjig

std ji∑∑ −

=

2)),((

6.2

The standard deviation represents the variation of grey level value in comparison with the mean

value m.

Chapter 6

- 45 -

3. Skewness (sk) 3

3)),((1

std

mjig

Nsk ji

∑∑ −

= 6.3

The skewness describes the degree of histogram asymmetry around the mean.

4. Kurtosis (k) 4

4)),((1

std

mjig

Nk ji

∑∑ −

= 6.4

Kurtosis describes the sharpness of the grey level histogram.

6.4.2 Second Order Statistical Features

Features resulting from the 2nd order statistics provide information regarding the spatial

relationship between various grey level values within thyroid nodule. These textural features were

derived from the co-occurrence and run-length matrices [73,74].

6.4.2.1 Co-Occurrence Matrix Features

In the co-occurrence matrices, grey level pixels are considered in pairs with a relative distance (d)

and orientation φ among them [73]. The orientation φ is quantized in four directions (00, 450, 900,

1350). An example of co-occurrence matrix computation is depicted in Figure 6.1.

0 0 2 2 1 1 0 0 3 2 3 3 3 2 2 2

(a)

Grey tones 0 1 2 3

0 (0,0) (0,1) (0,2) (0,3) 1 (1,0) (1,1) (1,2) (1,3) 2 (2,1) (2,2) (2,3) (2,4)

Gre

y to

nes

3 (3,1) (3,2) (3,3) (3,4) (b)

Co-Occurrence φ=00

4 1 1 0 1 2 0 0 1 0 6 3 0 0 3 2

Co-Occurrence

φ=450

0 1 2 1 1 0 1 1 2 1 0 3 1 1 3 0

Co-Occurrence

φ=900

0 2 2 2 2 0 1 1 2 1 2 2 2 1 2 2

Co-Occurrence

φ=1350

2 1 1 1 1 0 1 1 1 1 2 2 1 1 2 0

(c) (d) (e) (f)

Figure 6.1 (a) Image array with four grey levels. (b) General form of any grey-tone co-

occurrence matrix. (c)-(f) Computation of all four co-occurrence matrices with distance d=1.

Pattern Recognition

- 46 -

Let an image array I(m,n) with four grey levels (Ng=4) ranging from 0 to 3. Figure 6.1(b) depicts

the general form of any grey tone co-occurrence matrix. For example, the element in the (0,0)

position of a distance d=1 is the total number of times two grey tones of value 0 and 0 occurred

along the four quantized directions adjacent to each other. Figures 6.1(c) - 6.1(f) demonstrate all

possible grey tones combinations with distance set to 1 along all four directions.

The textural features that can be extracted from the co-occurrence matrices are presented below:

1. Angular Second Moment (ASM) ∑∑−

=

−

=

=1

0

1

0

2)),((gN

i

gN

j

jipASM 6.5

where Ng is the number of grey levels in the image, i,j=1,…,Ng, and p(i,j) is the co-occurrence

matrix. The ASM feature describes the degree of homogeneity within the thyroid nodule and takes

small values in regions with no variability.

2. Contrast (CON) njijipnCONgN

i

gN

j

gN

n

=−⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

= ∑∑∑−

=

−

=

−

=

,)),((1

0

1

0

2

1

0

2 6.6

Con feature describe the amount of local variations present within the nodule and takes high

values in regions great variability. The factor n2 enhances any possible existence of local

variations.

3. Inverse Different Moment (IDM) ∑∑−

=

−

=−+

=1

0

1

02)(1

),(gN

i

gN

j jijipIDM 6.7

IDM feature takes high values for low-contrast images due to the inverse (i-j)2 dependence.

4. Entropy(ENT) ( )∑∑−

=

−

=

−=1

0

1

0

),(log),(gN

i

gN

j

jipjipENT 6.8

ENT feature describes the degree of randomness and takes low values for smooth images.

5. Correlation(COR) yx

gN

i

gN

jyx mmjipij

CORσσ

∑∑−

=

−

=

−

=

1

0

1

0

),()(

6.9

where mx,my,σx,σy are the mean values and standard deviations of px and py (equations …)

respectively. COR feature describes the spatial dependencies of the grey tones within the thyroid

nodule.

∑=

=rowsN

ix jipip

1

),()( 6.10

Chapter 6

- 47 -

∑=

=columnsN

jy jipjp

1

),()( 6.11

Other features derived from the co-occurrence matrices are:

6. Sum of Squares (SSQ) ∑∑−

=

−

=

−=1

0

1

0

2 ),()1(gN

i

gN

j

jipmSSQ 6.12

7. Sum Average (SAV) ∑=

+=gN

iyx iipSAV

2

2

)( 6.13

where px+y is

∑∑−

=

−

=

+ ==+=1 1

1

2,...,3,2,),,()(gN

iig

gN

jyx Nkkjijipkp 6.14

8. Sum Entropy (SENT) ( )∑=

++−=gN

iyxyx ipipSENT

2

2

)(log)( 6.15

9. Sum Variance (SVAR) ∑=

+−−=gN

iyx ipSENTiSVAR

2

2

2 )()( 6.16

10. Difference Variance (DVAR) ∑=

−−−=gN

iyx ipSAViDVAR

2

2

2 )()( 6.17

11. Different Entropy (DENT) ( )∑−

=

−−−=1

0

)(log)(gN

iyxyx ipipDENT 6.18

where px-y is

∑∑= =

− −==−=gN

iig

gN

jyx Nkkjijipkp 1,...,3,2,),,()(

1

6.19

12. Information Measure of Correlation (ICM1) HYHX

HXYHXYICM,max

11 −= 6.20

13. Information Measure of Correlation (ICM2)

2/1)])2(0.2exp[1(2 HXYHXYICM −−−= 6.21

where

( )∑∑−

=

−

=

−=1

0

1

0

),(log),(gN

i

gN

j

jipjipHXY 6.22

Pattern Recognition

- 48 -

( )∑∑−

=

−

=

−=1

0

1

0

)()(log),(1gN

i

gN

jyx jpipjipHXY 6.23

( )∑∑−

=

−

=

−=1

0

1

0)()(log)()(2

g gN

i

N

jyxyx jpipjpipHXY 6.24

6.4.2.2 Run-Length Matrix Features

The run length matrix encodes textural information based on the number each grey level appears

in the image by itself [74]. Let an image array I(m,n) with four grey levels (Ng=4) ranging from 0

to 3( Figure 6.2(a) ). For each direction (00, 450, 900, 1350) the corresponding run length matrix is

computed (Figure 6.2(b) - Figure 6.2(e)).

0 0 2 2 1 1 0 0 3 2 3 3 3 2 2 2

(a)

Run Length 00 1 2 3 4

0 0 2 0 0 1 0 1 0 0 2 1 1 1 0

Gre

y Le

vel

3 2 1 0 0


0 4 0 0 0 1 2 0 0 0 2 6 0 0 0

Gre

y Le

vel

3 4 0 0 0

(b) (c)


0 4 0 0 0 1 2 0 0 0 2 4 1 0 0

Gre

y Le

vel

3 2 1 0 0

Run Length 1350 1 2 3 4

0 2 1 0 0 1 2 0 0 0 2 4 1 0 0

Gre

y Le

vel

3 4 0 0 0

(d) (e) Figure 6.2 (a) Image array with four grey levels. (b)-(e) Computation of all four run length

matrices for texture analysis.

Each matrix element specifies the number of times that the picture contains a run of length (0…3)

in the given direction. The first element of the first row of the matrix is the number of times grey

level ‘0’ appears by itself, the second element is the number of times it appears in pairs and so on.

The textural features that can be extracted from the run length matrices are presented below:

Chapter 6

- 49 -

1. Short Run Emphasis(SRE)

∑∑

∑∑

= =

= ==g r

g r

N

i

N

j

N

i

N

j

jir

jjir

SRE

1 1

1 12

),(

),(

6.25

where r(i,j) is the run length matrix, Ng is the number of gray values in the image, Nr is the

largest possible run, i=1,…,Ng, j=1,…,Nr. SRE tends to emphasize short runs due to the division

with j2. It takes large values for nodules with high variability.

2. Long Run Emphasis(LRE)

∑∑

∑∑

= =

= ==g r

g r

N

i

N

j

N

i

N

j

jir

jirjLRE

1 1

1 1

2

),(

),( 6.26

LRE tends to emphasize long runs. It takes large values for nodules with low variability.

3. Grey Level Non Uniformity (GLNU)

∑∑

∑ ∑

= =

= =⎟⎟⎠

⎞⎜⎜⎝

⎛

=g r

g r

N

i

N

j

N

i

N

j

jir

jirGLNU

1 1

1

2

1

),(

),( 6.27

GLNU is proportional with large run length values that are uniformly distributed. It takes large

values for nodules with high variability.

4. Run Length Non Uniformity (RLNU)

∑∑

∑ ∑

= =

= =⎟⎟⎠

⎞⎜⎜⎝

⎛

=g r

r g

N

i

N

j

N

i

N

j

jir

jirRLNU

1 1

1

2

1

),(

),( 6.28

RLNU encodes long runs that are non-uniformly distributed. It takes small values for nodules with

high variability.

5. Run Percentage (RP) P

jirRP

g rN

i

N

j∑∑= == 1 1

),( 6.29

where P is the total possible number of runs in the nucleus image. This feature takes its lowest

value in nodules with low variability.

Pattern Recognition

- 50 -

6.4.3 Shape and Geometrical Features

Besides textural sonographic criteria of the thyroid nodule, various shape and geometrical

features such as irregular margins and circular boundaries are employed in the decision making

procedure. In the present thesis several geometrical and shape based features were computed in

order to quantify all the observations made by the physicians throughout the thyroid nodule

literature [72, 75, 76]. These features were:

1. Average Radius ( ) ( )( )

N

YoiyXoixRavg

N

i∑=

−+−= 1

22 )()( 6.30

Ravg is computed by averaging the Euclidean distance from the nodule’s centroid (Xo,Yo) to

each of the boundary points (x,y) (Figure 6.3).

Figure 6.3 Line segments used to compute radius.

2. Radius Standard Deviation ( )

N

RavgiRRST

N

i∑=

−= 1

2)( 6.31

RST encodes information regarding the irregularity of the nodule’s borderline. It takes high values

in cases where the boundary is not circular.

3. Perimeter NP = 6.32

P is measured by summing the number or pixels on the border of the nodule.

4. Area

Area is computed by counting the number of pixels on the interior of the nodule’s boundary.

5. Radial Entropy ∑=

=100

1

)log(k

kk ppRE 6.33

Chapter 6

- 51 -

where pk is the probability that the radius distance will be between d(i) and d(i) + 0.01d(i). The

parameter pk was computed by the radial histogram. The amplitude range between the minimum

and maximum values of the radius distance measure was divided into 100 bins and the number of

times the radius distance plot passed through each bin was summed. Afterwards the sums were

divided by the total number of samples.

6. Circularity or Roundness AreaPCirc

2

= 6.34

Circ is minimized for a circle and is proportional with the nodule’s shape irregularity.

7. Smoothness P

RRRSM

iiispo∑ +− +−

= 211

int

6.35

where the Ri, Ri-1 and Ri+1 are depicted in Figure 6.4. SM is computed by measuring the difference

between the length of a radius and the mean length of the two radiuses surrounding it. It takes

small values for nodules with regular borders.

Figure 6.4 Line segments used to compute Smoothness.

8. Concavity

∑

∑

=

=

−+−

−+−= M

iABCentroidABCentroid

N

iCVCentroidCVCentroid

ii

ii

XXYYM

XXYYNConcavity

1

22

1

22

)()(1

)()(1

6.36

Concavity is computed by measuring the size of any indentations in the thyroid nodule. In fact is

the average of the convex hull (CV) distances from the center (Centroid) of the nodule and the

distances from the actual nodule boundary (AB) (Figure 6.5). Apparently it takes minimum values

for circular or elliptical nodules.

9. Concave Points

Pattern Recognition

- 52 -

Concave points are the number of points in the actual nodule’s boundary that lies in the concave

region (Figure 6.5). The greater the number of concave points the more irregular the nodule’s

border.

Figure 6.5 Convex hull is used to compute concavity and concave points.

10. Average Convex Hull Radius ( ) ( )( )

N

YoiCHyXoiCHxRCHavg

N

i∑=

−+−= 1

22 )()( 6.37

RCHavg is computed by averaging the Euclidean distance from the nodule’s centroid (Xo,Yo) to

each of the convex hull boundary points (CHx,CHy).

11. Symmetry iii

iii

rightleftrightleft

SYM+Σ−Σ

= 6.38

SYM is computed by measuring the relative difference in length between pairs of line segments

perpendicular to the major axis of the nodule. The major axis is determined by finding the

diameter of the nodule and the line segments were drawn at regular intervals (Figure 6.6). It

encodes geometrical information regarding shape variability of the nodule [77,78].

Figure 6.6 Line segments used to compute Symmetry. The lengths of perpendicular segments on

the right of the major axis are compared to those on the left.

Chapter 6

- 53 -

12. Fractal Dimension

Fractal dimension of the nodule’s boundary is approximated using the box-counting method

[72,79,80].The perimeter of the nodule is measured using decreasingly smaller ‘rulers’ to

construct a box that contains the nodule. As the ruler size decrease, increasing the precision of the

measurement, the observed perimeter increases. Plotting these values on a log scale and

measuring the upward slope gives the approximation of the fractal dimension (Figure 6.7). Fractal

dimension is a measure of ‘how’ complicated is the boundary of the nodule.

Figure 6.7 Fractal dimension estimation. N is the number of covering boxes and s is the number

of ‘rules’ or the size (perimeter) of each box.

6.4.4 Local Maxima Features

A comprehensive study regarding the local maxima features employed in the present thesis is

presented in Chapter 10.

6.5 Data Normalization

In most cases the features values have different dynamic ranges. In order to overcome this

problem all features values are normalized so that they lie within similar dynamic ranges. The

normalization technique used in this thesis is made via the mean and variance of the feature

values [72,81].

k

ikikik

xxxσ−

=ˆ 6.39

Pattern Recognition

- 54 -

where ikx and ikx are the kth feature values before and after the normalization. ikx and kσ are the

mean value and standard deviation of the kth feature.

6.6 Classification Task

Given a specific classifier, classification performance is tested employing the leave-one-out

method and for all possible combinations (2’s, 3’s, etc) of the computed features during the

feature generation stage. The aim is to determine the optimum combination of features that

achieves the highest classification accuracy with the minimum number of features. According the

leave-one-out method, the classifier is designed by all but one the training sets of feature vectors.

The ‘left-out-feature’ vector is treated us unknown class and it is classified by the system. The

whole procedure is repeated until all feature vectors have been tested. Results are then presented

in a two way truth table or confusion matrix [82,83]. The classifiers designed throughout this

thesis are presented below.

6.6.1 Minimum Distance Classifiers

Minimum distance classifier: In the minimum distance classifier the pattern classes in the feature

space cluster around their respective means. The decision boundary which separates the two

patterns is the perpendicular bisector of the line joining both means. Each feature vector is

classified whether its positions is on the left or the right of the bisector [83]. The discriminant

function of the minimum distance classifier using Euclidean metrics is presented in the following

equation:

)(21)( T

jjT

j mmmxxd −= 6.40

where x is the input feature vector, and mj the mean value of class j.

Least square minimum distance (LSMD) classifier: The LSMD classifier maps via a non-linear

transformation the input data set into a decision space where each class is clustered around a pre-

selected point [83]. The classification of a given test point is based on its minimum distance from

each pre-selected point. For the LSMD, the discriminant function is given by:

gi(x) = j

d

jij x∑

=1α – αi(d+1) 6.41

where d is the number of features, αij are weight elements and xj are the input vector feature

elements.

Chapter 6

- 55 -

6.6.2 Bayesian Classifier

The Bayes decision theory develops a probabilistic approach to pattern recognition, based on the

statistical nature of the generated features. The Bayes discriminant function [72,83] for class i and

for pattern vector x is given by:

gi(x) = lnPi – 21 ln|Ci| – 2

1 [(x – mi)TCi-1(x – mi)] 6.42

where Pi is the probability of occurrence of class i, mi is the mean feature vector of class i, and Ci

is the covariance matrix of class i.

6.6.3 Neural Networks Classifiers

Artificial Neural Networks are basic input and output models, with the neurones organised into

layers. Simple perceptrons consist of a layer of input neurones, coupled with a layer of output

neurones, and a single layer of weights between them. The learning process consists of finding

the correct values for the weights between the input and output layer. The principle weakness of

simple perceptron was that it could only solve problems that were linearly separable. To obtain a

bilinear solution more layers of weights are added to the simple perceptron model obtaining the

multilayer perceptron network [83,84].

Multilayer Perceptron (MLP) Classifier: In MLP classifier [83,84] (Figure 6.8), each node of a

hidden layer or output layer and the output y(j) of node j is related to its input by:

)(e11)( jSjy −+

= 6.43

where ∑==

N

ijiwiyjS

1),()()( and w(i,j) are connections weights between the previous node i and

the current node j; y(i)w(i,j) is the weighted output of the previous node i, which is used as input

to node j; N is number of inputs to node j; and S(j) is the sum of all weighted inputs y(i)w(i,j) of

the previous layer to node j.

Pattern Recognition

- 56 -

Figure 6.8 Schematic diagram of the multilayer perceptron neural network employed, with two

input features, two classes, two hidden layers and four nodes in each hidden layer.

The connection weights w(i,j) between different layer nodes of the MLP are calculated iteratively

until they stabilize, by the following equation:

w(i,j)n+1 = w(i,j)n + αd(j)y(j) + z(w(i,j)n – w(i,j)n-1) 6.44

where (n+1), n, (n-1) correspond to next, present, and previous respectively, α, z are constants,

d(j) is the error between the desired t(j) and actual y(j), and is given by:

d(j) = (t(j) – y(j))y(j)(1 – y(j)) 6.45

and for a hidden layer node by:

d(j) = y(j)(1 – y(j))∑k

kjwkd ),()( 6.46

where k is associated with all layers nodes to the right of the current node j.

Probabilistic Neural Network (PNN) classifier: The PNN is implemented by a feed-forward and

one-pass structure (see Figure 6.9) and encapsulate the Bayes’s decision rule together with the use

of Parzen estimators of data’s probability distribution function. The discriminant function of a

PNN for class j is given by the following equation, as described at [84,85,86]:

( ) ( )∑=

−−−

=j ij

TijN

ijppj eN

g1

22/

2

)2(1)( σ

σπ

xxxx

x 6.47

Chapter 6

- 57 -

where x is the test pattern vector to be classified, xi is the i-th training pattern vector of the j-th

class, Nj is the number of patterns in class j, σ is a smoothing parameter, and p is the number of

features employed in the feature vector.

The PNN architecture comprises 4 layers (Figure 6.9). The input layer that has a node for each

feature of input data. The pattern layer in which, one pattern node corresponds to each training

pattern. The summation layer, which receives the outputs from pattern nodes associated with a

given class and the output layer which has as many nodes as the input classes. The test pattern x

is classified to the class with the larger discriminant function value.

Figure 6.9 Schematic diagram of the probabilistic neural network employed, with two input

features and two classes.

6.6.4 Support Vector Machines Classifier

A classifier based on support vector machines (SVM) [84,87,88] is a general classifier that it can

be applied to linearly as well to non-linearly separable data, with or without overlap between the

classes. In the most general case of overlapped and non-linearly separable data, the problem is (a)

to transform the training patterns from the input space to a feature space with higher

dimensionality (x ∈ Rd a Φ(x) ∈ Rh) where the classes become linearly separable, and (b) find

two parallel hyperplanes with maximum distance between them and at the same time with

minimum number of training points in the area between them (also called the margin). The

separating hyperplanes in the transformed feature space are defined by the following equation:

w⋅Φ(x) + b = ± 1 6.48

Pattern Recognition

- 58 -

where +1 is referred to class 1, –1 is referred to class 2, x if the pattern vector, w is the normal

vector to the hyperplanes, and b the bias or threshold which describes the distance of the decision

hyperplane from the origin (that is equal to b/||w||). The discriminant function is given by:

g(x) =sign(w⋅Φ(x) + b) 6.49

The parameters w and b are calculated as follows: Let N training pattern vectors xi ∈ Rd, i=1…N

(where d is the number of features) belonging to two classes identified by the label yi ∈ –1, +1.

The conditions for the hyperplanes may take the following mathematical formulation:

(i) minimize the number of training pattern vectors that lie between the two hyperplanes, so:

yi(w⋅Φ(x i) + b) + ξi ≥ 1 6.50

where ξi ≥ 0, i=1…N are real non-negative slack-variables.

(ii) the distance between the two hyperplanes (which is equal to 2/||w||) must be maximized, so

21 ||w|| must be minimized. The above conditions lead to minimizing 2

1 ||w||2 + ∑Cξi subject to

(6.49), where C is a positive constant that reflects a trade-off between the classification errors and

the size of the margin. Introducing Lagrangian multipliers αi, βi, i=1…N, the Lagrangian is given

by:

LP = ∑∑∑===

−−++⋅−+N

iiii

N

iiii

N

ii byC

111

2 )1))(((21 ξβξαξ xΦww 6.51

The problem is now to maximize LP subject to 0=∂∂

bLP , 0=

∂∂

wPL

and 0=∂∂

i

PLξ

(with

αi, βi ≥ 0). These constraints give respectively:

01

=∑=

N

iii yα 6.52

w = ∑=

N

iiii y

1

)(xΦα 6.53

and

C = αi + βi 6.54

The equation (A.7), in combining with αi, βi ≥ 0, results that 0 ≤ αi ≤ C. Substituting equations

(6.51, 6.52, 6.53) in relation with (6.50), we take the dual variables Lagrangian LD:

Chapter 6

- 59 -

LD = ∑∑==

⋅−N

jijijiji

N

ii yy

1,1)()(

21 xΦxΦααα 6.55

By use of a kernel function, that it can replace the inner product Φ(xi)⋅Φ(xj) in the higher

dimensional feature space, the dual Lagrangian LD can take the form of (6.55):

LD = ∑∑==

−N

jijijiji

N

ii kyy

1,1),(

21 xxααα 6.56

A function can be used as a kernel function if it satisfies the following Mercer’s condition:

“Any symmetric function k(x,y) in the input space is equivalent to an inner product in the feature

space, if ∫∫ ≥ 0)()(),( yxyxyx ddggk , for any function g(x) for which xx dg∫ )(2 < ∞ ”

Using equations (6.48), (6.52), and (6.55), it may be seen that ξi and βi have vanished, so the

discriminant function of the SVM classifier may be written as:

g(x) = ⎟⎟⎠

⎞⎜⎜⎝

⎛+∑

=

bkySN

iiii

1

),(sign xxα 6.57

where Ns is the number of pattern vectors (also called the support vectors) with non-zero αi’s.

Combining the equations (6.47), (6.52), and (6.55), the threshold b may be found as:

b = ∑ ∑= =

⎟⎠

⎞⎜⎝

⎛−

SN

j

N

ijiiij

S

kyyN 1 1

),(1 xxα 6.58

and the coefficients αi are obtained by solving the “dual” problem, which is maximization of LD

(equation (6.55)) subject to equation (6.51), with 0 ≤ αi ≤ C. Functions that are commonly used as

kernels are:

1. The linear kernel k(xi,xj) = xi.xj 6.59

2. The polynomial kernel k(xi,xj) = (xi.xj +θ )d 6.60

where d is the degree of the polynomial and θ an offset parameter,

3. The Gaussian radial basis kernel k(xi,xj) = ( ) ( ) ⎟⎠⎞⎜

⎝⎛ −−−

22exp

σJi

TJi xxxx 6.61

where σ is the standard deviation.

4. The sigmoidal kernel k(xi,xj) = tanh(κ(xi.xj) + θ ) 6.62

where κ the gain and θ the offset.

Pattern Recognition

- 60 -

5. The inverse multiquadric kernel k(x,y) = ((xi – xj)T(xi – xj) + c2) 21− 6.63

where c a non-negative real number.

6. The wavelet kernel ∑=kj

kjkj yxyxK,

,, )()(),( ψψ 6.64

where kj ,ψ is a translated wavelet of resolution j.

- 61 -

CHAPTER 7

Wavelet-Based Speckle Suppression in Ultrasound Images

Summary

In this chapter a wavelet-based method for speckle suppression in ultrasound images of the

thyroid gland is introduced. The chapter is organized as follows: At first an extensive review

of the literature regarding noise reduction in US images is presented. Afterwards, the speckle

model adopted by this study is presented followed by the proposed strategy based on the

inter-scale wavelet analysis. In the results section the speckle removal efficiency and edge

preserving are compared to that of current speckle suppressing methods. Moreover 63 US

images of the thyroid gland are subjected to review by 2 experienced observers via

questionnaire for qualitative evaluation of the proposed despeckling process. In the last

section an extensive discussion regarding the proposed algorithm is given.

7.1 Review of the Literature

A variety of speckle reduction techniques have been implemented in the past two decades.

Part of them reduce speckle by acquiring the radio frequency (RF) pulse echo signals from the

US devices directly after log compression and time gain compensation (TGC) and before scan

conversion [89,90]. However, access to raw RF data is somewhat complex and sometimes

impossible, especially in modern US scanners, which in turn renders the application of such

methods difficult for research purposes.

In the early years of computer image processing speckle removal in US images was achieved

via simple averaging, median filtering and Wiener filtering [91]. Simple averaging not only

failed to eliminate speckle but introduced blurring and edge loss in areas where anatomic

boundaries prevail. Median filtering enhances edges and speckle indiscriminately, while

Wiener filter manages to remove considerable amounts of speckle but also tends to over-

smooth the boundaries of important image features. Various adaptive filters based on local

statistics, such as mean and variance, have been implemented for noise reduction not solely in

medical imaging but for image denoising in general [92,93,94]. As the computing technology

boosted during the ‘90s, along with the processors speed and power, new and more

complicated filters were introduced. They were employed mainly in time domain such as the

adaptive-weighted median filter by Loupas et al. [95], the segmentation based L-filtering by

Kofidis et al. [96], the adaptive speckle suppression by Karaman et al. [97], the aggressive

region growing method by Chen et al. [98], the symmetrical speckle reduction filter by Huang

et al. [99] and the diffusion stick model by Hiao et al. [100].

Wavelet-based speckle suppression in ultrasound images

- 62 -

Loupas introduced a new class of non-linear adaptive filters employing some local statistics,

such as the ratio of m/2σ where σ, m are the local variance and mean inside a moving window

with pre-specified dimensions. Through these local statistical parameters the adaptive filter

was turned into a general low pass filter in homogenous areas and into an enhanced median

filter into areas with small structures or boundaries. Karaman’s method depended on the same

statistical principles employed by Loupas regarding the moving window and its local

statistics. The filter was transformed into a mean filter or a median depending on an estimated

homogeneity criterion. Kofidis segmented the US image to various stationary regions

employing a combination of the Learning Vector Quintizer (LVQ) and the maximum

likelihood estimator of the original noiseless signal (L2 mean). Subsequently, these subimages

are filtered by a set of L-filters. L-filter design process is based on order statistics (i.e.

autocorrelation matrix) derived from the previous stage.

Chen presented a new region growing filtering method based on a trade off between a

trimmed mean filter and a median filter. In order to overcome some of the limitations of the

above methods he added an adaptive homogeneity criterion. Through this criterion a

homogenous area is differentiated from a heterogeneous area, thus altering the filter applied to

that area to mean or median respectively. Huang divided his filtering strategy based on the

slope facet model in two stages: firstly he introduced two criteria in the region growing

process to approximate the largest despeckling window within an 11x11 matrix. The first is

the widely used variance to mean criterion and the second is the gradient criterion. In the

second stage after the major removal of speckle he used only the gradient criterion for the

final noise elimination. In both stages the filter acts generally as common mean filter.

Xiao exhibits an interesting oriented filter with 24 asymmetrical diffusion sticks inside a

symmetric moving matrix. Through a variation function applied in every stick, the algorithm

smoothes the sticks with high homogeneity and penalizes smoothing within heterogeneous

regions. The smoothing function comprised the weighted sum of averages along each stick.

For optimization of the results the whole filtering process is done iteratively. The empirical

choice of some parameters such as window size, weight calculation, homogeneity criterion or

various thresholds employed of the above mentioned methods degraded their generalization

ability thus made them US machine and anatomical region depended.

In the past decade a new approach in US images denoising emerged based on the wavelet

transform. Some of the wavelet based proposed methods for US image despeckling, are the

homomorphic wavelet shrinkage by Zong et al. [101], the multiscale nonlinear processing

method by Hao et al. [102], and the Bayesian wavelet method by Achim et al. [103]. Zong

applied Mallat’s Dyadic Wavelet transform [62] on a US image, which is logarithmically

transformed due to the multiplicative nature of speckle. In the resulted decompositions he

applied a combination of soft and hard thresholding, introduced by Donoho [104], at fines and

Chapter 7

- 63 -

middle scales respectively in order to eliminate the presence of speckle. Besides wavelet

coefficients shrinkage, Zong achieved boundary enhancement by means of an adaptive gain

operator and some predefined thresholds.

Hao presented a combination of Loupas method and wavelet transform shrinkage. Initially, he

divided the image via the adaptive-weighted median filter in two parts that approximate signal

and noise. These two parts are decomposed through the wavelet transform and a modification

of Donoho’s soft thresholding is used to remove speckle. The final denoised image is the sum

of the two reconstructed image parts, into which the original image was split in the first stage.

Both methods are mainly adopting the denoising thresholding procedure presented by

Donoho. In this method thresholds are calculated empirically and in an ad hoc manner

without taking into account the special statistical properties of speckle.

Achim in his attempt to overcome the limitations arising from empirical thresholding of

wavelet coefficients employed a Bayesian approach for signal extraction and speckle

suppression. The log-transformed US image was decomposed in different frequency scales

via the wavelet transform. In each scale a Bayesian estimator is used, based on symmetric

alpha stable distribution of the wavelet decomposition, to differentiate the signal coefficients

from the noise coefficients.

Besides US images, speckle dominates Synthetic Aperture Radar (SAR) images as well,

introducing difficulties on their correct interpretation. Various attempts are made in the

wavelet domain in order to efficiently reduce the resulting granular pattern. Sveinsson et al

[105] and Pantaleoni et al [106], via orthogonal wavelet transform and the Daubechies

wavelet family, applied soft thresholding and the enhanced Lee filter respectively on the

wavelet coefficients to reduce the presence of speckle. The aforementioned wavelet-based

approaches use the logarithmic transform to convert the multiplicative model of speckle into

additive model with signal – independent noise before performing the speckle reduction

method. After that, an exponential transform is applied to convert the denoised image to its

original format. The fact that the mean of the log transformed speckle noise is not zero,

whereas additive white Gaussian noise (AWGN) is considered with zero mean from the above

methods, led to the need of a correction step regarding the mean bias in the processing stages,

to avoid distortion in the de-speckled image [107].

Several recent studies avoid the log transform and directly apply the wavelet transform onto

the SAR images. Foucher et al [108] in order to discriminate reflectivity coefficients from

speckle coefficients implemented a Bayesian analysis based on the Pearson system for

probability density function (pdf) approximation of the wavelet coefficients. Argenti et al

[109] applied a minimum mean-square error (MMSE) filtering in the un-decimated wavelet

domain to suppress speckle noise coefficients and Dai et al [110] combined a Bayesian

shrinkage factor and a ratio edge detector applied in the wavelet coefficients for speckle


- 64 -

reduction with edge preservation in homogenous areas. An efficient discrimination between

speckle noise and reflected signal in US or SAR images either in time or wavelet domain is

still under discussion in the scientific society. As already mentioned an accurate despeckling

algorithm is very important in the decision making process especially in US images of the

thyroid gland. Often, thyroid nodules, which play the most important role in estimating the

malignancy risk factor, are of low contrast in a noisy background. Likewise the presence of

various structures inside the nodules comprises a critical factor for a proper interpretation of

the US image. The dominating speckle noise in all US images can lead to misleading analysis

thus obstructing the physician’s diagnosis.

7.2 Materials and Methods

7.2.1 Overview and Implementation of the Algorithm

A wavelet based method is introduced in this thesis for efficient speckle suppression in

sonographic images of the thyroid gland while important edges and boundaries are preserved.

The proposed wavelet approach avoids both log and exponential transform, considering the

fully developed speckle as additive signal-dependent noise with zero mean. The proposed

method throughout the wavelet transform has the capacity to combine the information at

different frequency bands and accurately measure the local regularity of image features. The

inter-scale information is acquired by means of a coarse to fine connectivity of the wavelet

transform modulus maxima (WTMM). Two structures, represented by the modulus maxima,

in two consecutive scales belong to the same anatomic area if the pair ‘position & angle’ pixel

of the maximum wavelet coefficient value in the upper scale is also approximately present in

the lower scale. The decay across scales of wavelet transform maxima is related to local

regularity of these structures and is assessed by the Lipschitz exponent “a” [70]. The purpose

of the present study is to employ the knowledge given from the evolution of the wavelet

transform maxima across scales to discriminate image singularities from speckle singularities.

All the proposed method’s steps (i.e Redundant wavelet transform, multiscale edge

representation, coarse to fine analysis together with the wavelet coefficient and maxima

display) were all implemented in Matlab 6.5. The methods to which the proposed algorithm is

compared with were also implemented and integrated with the same software packet. The

computer used for processing has an AMD Athlon XP+ processor running at 1.8 GHz and 512

of RAM. The ultrasound system used for this study was the HDI-3000 ATL digital ultrasound

system with a broadband linear array with 7 MHz central frequency. The digitization of the

output Video signal of the ultrasound system was made via the video card Miro

PCTV(Pinnacle Systems), which is installed in a PC. US images are stored in JPEG format

and their size is 768 x 576 x 8. The primary steps of the proposed method are illustrated in

Figure 7.1.

Chapter 7

- 65 -

Multiscale EdgeRepresentation

Function RegularityEstimation

'Atrous' DWT

Modulus Maxima

Gradient VectorComputation

Coarse to FineInterscale Analysis


IDWT De-SpeckledImage

SpeckleImage

Figure 7.1 Block Diagram of the proposed wavelet based algorithm for speckle suppression.

7.2.2 Speckle Model

Despite the profound advantages of ultrasonography, US images carry a granular pattern, so

called speckle, which constitutes a major image quality degradation factor. Speckle pattern is

created when an ultrasonic wave with uniform intensity is incident either on a rough surface

or on tissue particles that are spaced at less than the axial resolving distance of the US system.

In that case, the reflection beam profile will not have a uniform intensity. Instead it will be

composed of many regions with strong and weak intensities. This complex intensity profile

arises because sound is reflected in many different directions from the rough surface or from

the small scatterers, thus leading US waves that have travelled different scan lines to interfere

constructively and destructively towards the ultrasonic transducer. The intensity fluctuations

within a uniform anatomic area, caused by the above phenomenon, constitute speckle [111].

The resulting degraded by speckle US image does not correspond to the actual tissue

microstructure. In fact, speckle noise deteriorates image quality, fine details and edge

definition. Speckle also tends to mask the presence of low-contrast lesions, therefore reducing

the physician’s ability for accurate interpretation. Moreover, it constitutes a limiting factor in

the performance of quantitative procedures such as segmentation and pattern recognition

algorithms. Hence, effective speckle suppression is considered of value for improving US

image quality and possibly the diagnostic potential of medical ultrasound imaging, except in

rare cases of abdominal and breast US images where the presence of speckle may assist in

assessing liver cirrhosis or breast cancer [112,113].

The speckle model employed in the despeckling strategies in time domain [95,97,98,99,

100,102] considers the envelope detected RF signal having a Rayleigh distribution, thus

speckle can be considered as multiplicative noise. However, due to US device’s undergoing

signal processing stages, the finally formatted US image speckle is no longer multiplicative

and can be thought as Gaussian additive noise independent of the noise-free signal. Most


- 66 -

wavelet – based methods [101,103,105,106,70], adapted for additive Gaussian white noise,

applied a logarithmic transform in the speckle image and approximated speckle as additive

noise.

The proposed method adopted Foucher et al [108], Argenti et al [109] and Dai et al [110]

approaches, by omitting the log-transform to avoid the mean bias correction problem and

decomposing the multiplicative speckle model into an additive signal dependent noise model.

The multiplicative speckle model at pixel position [x,y] is expressed in the following form:

),(),(),( yxryxfyxI ⋅= 7.1

where f(x,y) is an unknown 2-d function, such as the original image to be recovered without

noise. I(x,y) is the corrupted with noise formatted US image, and r(x,y) a random variable that

represents speckle. We consider speckle as fully developed (large number of small scatterers

in each resolution cell) whose magnitude follows the Rayleigh pdf [114]:

0,4

exp2

)(2

≥⎟⎟⎠

⎞⎜⎜⎝

⎛−= rrrrprππ

7.2

Its mean and variance are [114]:

1)( =rE , 14)var( −=π

r 7.3

We convert the multiplicative model into an additive model:

]1),()[,(),(),( −+= yxryxfyxfyxI

),(),( yxNyxf σ+= 7.4

Where ]1),([ −yxr is a random variable with zero mean and variance 2σ

),( yxNσ represents an additive signal dependent noise term, which is proportional to the

signal to be estimated.

Chapter 7

- 67 -

7.2.3 Inter-Scale Wavelet Analysis

7.2.3.1 Dyadic Wavelet Transform

Employing wavelet theory, the correlation of the inter-scale edge information may be applied

to characterize different types of edges. Wavelet analysis was performed by means of the

Dyadic Wavelet Transform (DWT) introduced by Mallat and Zong [62] for characterization

of signals from multiscale edges. DWT is based on a wavelet function ψ(x) with compact

support, which is the first order derivative of cubic spline function. The wavelet

decomposition across scales of the original image was implemented with a filter bank

algorithm, so called ‘algorithme a atrous’ (algorithm with holes). The proposed transform is

in fact a fast bi-orthogonal discrete wavelet transform, in which the size of the decomposed

sub-band images is the same as that of the original image thus making the transform highly

redundant.

Let ),( yxθ be a symmetrical smoothing function approximating the Gaussian. The two-

dimensional Dyadic Wavelet Transform of a function )(),( 22 RLyxf ∈ is the set of

functions )),(),,(( 22

12

yxfWyxfW jj , which are respectively the partial derivative along the

horizontal and vertical orientation of the convolution of ),( yxf with the smoothing

function ),( yxθ dilated along a dyadic sequence Ζ∈jj )2( . The DWT is given by:

( )( )

( )( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∗∂∂

∗∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛∗=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

yxfy

yxfxf

yxfWyxfW

j

j

j

j

j

j j

,

,2

),(),(

2

2

22

12

2

1

2

2

θ

θ

ψψ

7.5

where ),(1 yxψ and ),(2 yxψ are the analyzing wavelets and j the dyadic scale.

We performed the dyadic wavelet transform using Mallat’s filters. These filters are suitable

for fast implementation of discrete algorithms and they offer exact reconstruction. At a

dyadic scale j the dilation of the discrete filters is obtained by inserting (2j-1) zeros (holes)

between each of the coefficients of the corresponding filters. In Figure 7.2 the wavelet

decomposition with the ‘atrous algorithm’ in 3 dyadic scales of a US image of the thyroid

gland is presented.


- 68 -

Figure 7.2 At the top is the original US image. The two columns show respectively the

horizontal and vertical wavelet transform 312

23112

),(,),( ≤≤≤≤ jj yxfWyxfW jj along three

dyadic scales. The scale increases from top to bottom.

The redundant wavelet transform presented is in fact shift-invariant and it is widely used for

pattern recognition, feature extraction and edge detection purposes. The wavelet coefficients

Chapter 7

- 69 -

comprise the intensity profile of an image’s local variations for a given scale. They can be

considered as a classification map in which any kind of change (abrupt or smooth) exist in an

image can be localized on a particular scale. The latter conclusion indicates the importance of

an accurate selection of the dyadic scale j in which the image will be decomposed. The choice

of that scale is in fact a trade off between the suppression of wavelet coefficients

characterizing image’s irregularities and the blurring effect caused by the dilation of the

smoothing function. In small scales the wavelet coefficients mostly characterize high

frequency events mainly caused by noise. In bigger scales low frequency events are detected

such as smooth image variations.

7.2.3.2 Gradient Vector

Equation 5 indicates that the above set of functions can be viewed as the two components of

the gradient vector of ),( yxf smoothed by ),( yxθ at each scale j2 :

),)(*(2),(),(

22

1

2

2 yxfyxfWyxfW

j

j

j j θ→

∇⋅=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ 7.6

The modulus – angle representation of the gradient vector is given by:

22

222

12 ),(),(),( yxfWyxfWyxfM jj

j += 7.7

and

),(),(

arctan),( 22

12

2 yxfWyxfW

yxfAj

j

j = 7.8

7.2.3.3 Modulus Maxima

The sharper variation points of ),(*2

yf j χθ at a scale j2 correspond to edges, are obtained

from the local maxima of ),(2

yxfM j along the gradient direction given by ),(2

yxfA j .

At each scale j2 of the Dyadic Wavelet Transform, the point (x,y) where the modulus of the

gradient vector ),(2

yxfM j is maximum compared with its neighbor’s locally positioned in

the direction specified by ),(2

yxfA j , is called modulus maxima (Figure 7.3).


- 70 -

Figure 7.3 At the top is the original US image. The first column displays the modulus

images ),(2

yxfM j . High intensity values correspond to black pixels whereas low intensity

values to white pixels for optimized visual interpretation of the results. At the second column

the angle images ),(2

yxfA j are shown. The angle value turns from 0 (white) to 2π (black)

along the circle contour. At the last column, the image points where ),(2

yxfM j has local

Chapter 7

- 71 -

maxima in the direction indicated by ),(2

yxfA j are presented (black pixels). Each time such

a point is detected, the position of the resultant local maxima is recorded as well together with

the values of the modulus ),(2

yxfM j and angle ),(2

yxfA j at the corresponding locations.

7.2.3.4 Lipschitz Regularity

The aim of the present study is to efficiently characterize the image’s singularities, via an

inter-scale wavelet analysis, in order to discriminate speckle-noise from signal. The

classification of singularities depends upon their local regularity. This regularity is quantified

by Lipschitz exponents [68]. A function f(x,y) is said to be Lipschitz α, 0 ≤ α≤ 1, at (x0,y0) if

there exists K>0 such that for all points 2),( Ryx ∈ :

( ) 2/20

2000 ),(),(

ayyxxKyxfyxf −+−≤− 7.9

If there exists a constant K>0 such that equation (9) is satisfied for any Ω∈),( 00 yx , then f is

uniformly Lipschitz a over Ω. The larger the a, the more regular is the function. Τhe Lipschitz

regularity of a function f(x,y) is related to the asymptotic decay from coarse to fine scales of

it’s wavelet transform along horizontal and vertical directions |W1f(u,v,s)| and |W2f(u,v,s)| in

the corresponding neighborhood. This decay is controlled by the wavelet transform local

maximum value Mf(u,v,s) [70]. A function f (x, y) is uniformly Lipschitz α , 0≤ α≤ 1 inside a

bounded domain of R2 if and only if there exists a constant A >0 such that for all (u ,v) inside

this domain and for any dyadic scale s relation 10 holds:

1),,( +≤ aAssvuMf 7.10

By measuring from (10) the Lipschitz exponent a through the computation of the decay slope

of log2|Mf(u,v,s)| we derive an estimate of the Lipschitz regularity along the edge.

7.2.3.5 Detection of Singularities

All singularities of f(x,y) can be located by following the wavelet transform modulus maxima

up to the finer scale. The terms coarse and fine are relative. Conventionally, coarse scales are

referred to bigger dyadic scales (23, 24), whereas fine scales are referred to smaller dyadic

scales (21, 22). The main objective of that inter-scale analysis is to isolate different structures

exist in the image, beginning at a coarse scale and adaptively decrease the scale to gather the

necessary details. If an edge appears in a coarser level 2j, it should also appear in finer level 2j-

1. The latter can be rephrased that any wavelet transform modulus maximum at a coarse scale

belongs to a connected inter-scale chain that is never interrupted when the scale decreases

[70], which in turn means that any structure – represented by the corresponding maxima – is


- 72 -

located in a coarse scale can also be found in a finer scale with an approximate position and

angle value.

Mallat [62,68] implements the maxima chaining procedure starting from a scale 2j and

considers that it propagates to coarser scale 2j+1 having similar position and angle values. In

this study the forming of maxima chains in the scale-space domain is made with a back-

propagation approach starting the inter-scale connectivity from the coarser scale (23)

computed and complete it at the finer scale (21) available. With this approach the

computational complexity of the implemented algorithm is reduced even more since we

employ the inter-scale exhaustive search with the smaller possible number of local maxima

(as the scale increases the number of local maxima decreases).

Before we apply this back-propagation tracking of modulus maxima in wavelet space, the

majority of some false maxima at the coarser scale (23) – that either are not suppressed by the

smoothing function or created by numerical errors in regions where the wavelet transform is

close to zero – are removed through a simple 70th percentile thresholding (all maxima values

below the 70% of the maximum modulus value are discarded) [115]. The chaining of

modulus maxima, after the thresholding procedure, across scales employs a two-folded inter-

scale investigation based on the parameter pair: position – angle. Two modulus maxima at

two successive scales [(Xk,Yk,Mk,Ak)2j, (Xk,Yk,Mk,Ak)2j-1] are chained if they have a close

position in the image plane(Xk,Yk) and similar angle value(Ak). If a single coarse local

maximum computed to back-propagate in more than one finer local maxima, only the one

having the largest maximum (Mk) is considered to belong to the maxima chain.

The maxima – matching between different scales was not an easy task. The position – angle

investigation was implemented at each scale within a different neighbourhood taking into

account the different size of the decomposition Mallat’s filter (different number of zeros

‘holes’ between the coefficients). The coarse information is traced within large

neighbourhoods whereas the fine information in small neighbourhoods. The adaptively

decreasing investigation window from coarse to fine scales avoids matching errors created

either from small maxima groups that might not constitute an exact match or large maxima

groups that may produce inaccurate inter-scale linking if the two successive structures are

locally distorted. A square window of width K at a coarse resolution 2j corresponds to square

windows with approximate size of K/2 and K/4 at finer resolutions 2j-1 and 2j-2 (Figure 7.4)

Chapter 7

- 73 -

Figure 7.4 Inter-scale back-propagation maxima connectivity in wavelet space.

At each of the maxima chains, acquired from back-propagation tracking, the decay of the

modulus maxima amplitude across scales is calculated in order to discriminate speckle

singularities from image singularities. In maxima chains where the amplitude of the wavelet

transform modulus maxima decreases when the scale decreases the Lipschitz regularity is

positive (positive Lipschitz exponents). On the contrary, when the maxima amplitude

increases when the scale decreases the Lipschitz regularity is negative (negative Lipschitz

exponents). The Lipschitz regularity was calculated between those scales in which the

amplitude of the decay slope was the greater. In our case was between the 23 & 22 scales. The

different decay behaviour of the modulus maxima is the main criterion in an accurate

discrimination of image and noise singularities. Image singularities belong to regular curves

with positive Lipschitz regularity that varies smoothly along these curves. Speckle

singularities give rise to negative Lipschitz regularity and considered as irregular variations of

the positions, angle and modulus values of the maxima.

The propagating maxima chains with positive Lipschitz regularity can be considered as an

edge map that corresponds to important image structures. The despeckling procedure

implemented in this article removes all wavelet coefficients at all scales that correspond to

those maxima whose amplitude increase when the scale decreases or do not belong to a back-

propagating maxima chain. The maxima recognized by the algorithm as speckle and as edges

for all scales are presented in Figure 7.5.


- 74 -

Figure 7.5 At the first column are the wavelet transform modulus maxima (non-propagating

maxima and propagating maxima with negative Lipschitz exponents) classified as speckle. In

the second are the propagating maxima with positive Lipschitz exponents classified as

important edges.

75

The remaining coefficients at all scales including the coarse image for completeness are

utilized in the inverse Dyadic Wavelet Transform to obtain the speckle suppressed US image.

The ability to isolate all important structures at all scales (figure 7.5 – right column) via the

proposed wavelet inter-scale analysis gave us the opportunity to perform the despeckling

strategy (maxima removal) at all computed scales, even at the finer one (21), contrary to

Mallat [29] which avoids to incorporate that scale to his denoising procedure due to signal

domination from noise. In our method as we can see in figure 7.5 – left column although at

the finer scale (21) available the human eye cannot discriminate the contours of the anatomical

structures, after the back-propagation tracking and singularity detection, in the same scale

these contours with approximate positions and angles became prominent.

7.3 Experimental Results and Evaluation

The effectiveness of the introduced wavelet based de-speckling approach was tested using a

tissue mimicking digital phantom and a US image of the thyroid gland. An observer

evaluation study was also undertaken involving 63 US thyroid images of 63 patients via a

questionnaire regarding the performance of the proposed algorithm. The proposed inter-scale

wavelet analysis method was compared with three representative denoising methods: (a)

Karaman’s adaptive speckle suppression filter ASSF [97] (b) Donoho’s soft thresholding and

(c) Donoho’s hard thresholding [104]. Wavelet shrinkage was implemented with Daubechies

8 mother wavelet in three decomposition scales, produced by the wavelet toolbox in matlab.

The quantification of the speckle suppression performance of all methods (in both phantom

and thyroid US image) was carried out by means of the speckle index (SI: mean to standard

deviation), on a homogenous area with uniformly distributed echoes, and the signal-to-mean-

square-error ratio (S/mse), introduced by Cagnon [116], on the same homogenous area (Local

region of interest) and on the entire image (Total). S/mse is defined as:

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ −

=

∑

∑

=

∧

=K

iii

K

ii

II

ImseS

1

1

2

10log10 7.11

Where, I are the intensity values of the speckle image, ∧

I are the intensity values of the de-

speckled image and K is the image size. The S/mse index can be considered as an index of

signal-to-noise within an image. High S/mse index values refer to efficient speckle

suppression while low to inadequate performance. The S/mse index is expressed in dB.

The evaluation of the edge preservation capacity, both locally (area where boundaries prevail)

and totally (entire image), of all methods was made by means of the parameter β, which has

been introduced by Hao [102] as shown in relation (7.12):


76

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛Δ−ΔΔ−ΔΓ⋅⎟

⎠⎞

⎜⎝⎛ Δ−ΔΔ−ΔΓ

⎟⎟⎠

⎞⎜⎜⎝

⎛Δ−ΔΔ−ΔΓ

=∧∧∧∧

∧∧

IIIIIIII

IIII

,,

,β

7.12

Where: ∧

ΔΔ II , are speckle and de-speckled images respectively, filtered by a 3x3 pixel

standard approximation of the Laplacian operator, and Γ is given by:

( ) ∑=

⋅=ΓK

iii

IIII1

2121 , 7.13

In case of optimum edge preservation, β approximates to 1. The closer the β is to 1 the better

are the edge preservation properties of each algorithm.

7.3.1 Tissue Mimicking Phantom Validation

The phantom used in this study was the 403 LE model manufactured by GAMMEX. It

comprises of three groups of three anechoic cystic targets (approximating thyroid nodules)

with 2, 4 and 6 mm diameter positioned at 3, 8 and 14 cm respectively. The attenuation

coefficient for the tissue mimicking materials is 0.5 dB/cm/MHz whereas for the anechoic

cysts is 0.05 dB/cm/MHz. Regarding the phantom image, the value of SI prior to despeckling

was 7.18 and the values of SI, S/mse and β after despeckling are shown in Table 7.1.

Table 7.1 Image quality measures obtained by four denoising methods tested on a digital

ultrasound phantom image

Method SI (Percentage

Improvement)

S/mse (Local/ Total) (dB)

β (Local / Total) (dB)

ASSF 6.98 (12%) 13.4912 / 12.7728 0.2148 / 0.1458

Soft Thresholding 7.33 (18%) 15.6425 / 16.7709 0.7020 / 0.7453

Hard Thresholding 7.11 (15%) 13.7175 / 15.1853 0.7764 / 0.8013

Wavelet inter-scale analysis Denoising

7.50 (21%) 17.9677 / 18.3241 0.8395 / 0.8485

7.3.2 US Image Case Study

All despeckling methods were also applied to an US image of the thyroid gland and their

results are demonstrated in Figure 7.6.

Chapter 7

77

Figure 7.6 (a) US image of the thyroid gland. (b) ASSF method, (c) wavelet shrinkage with

soft thresholding, (d) wavelet shrinkage with hard thresholding, (e) wavelet inter-scale

analysis denoising.

Both parameters (S/mse & β) are calculated locally and totally. The selected regions are


78

presented in Figure 7.7. The values of S/mse and β for all methods applied to the US image

are given in Table 7.2. The Si value prior to despeckling was 3.49.

Figure 7.7 Locally selected area containing the thyroid nodule – Box A for β calculation.

Locally selected area corresponding to homogenous tissue – Box B for S/mse calculation.

Table 7.2 Image quality measures obtained by four denoising methods tested on an

ultrasound image of the thyroid gland

Method SI (Percentage

Improvement)

S/mse (Local /Total) (dB)

β (Local /Total) (dB)

ASSF 3.98 (14%) 11.2871/10.5664 0.6020/0.3592

Soft Thresholding 4.15 (19%) 14.0577/14.5472 0.6705/0.7063

Hard Thresholding 4.05 (16%) 10.4593/11.4083

0.7602/0.7836

Wavelet inter-scale analysis Denoising

4.30 (23%) 15.4256/16.2937 0.8225/0.8490

A more detailed description regarding despeckling and edge preservation may also be

obtained by the profile signals depicted in Figure 7.9 derived from figure 7.6. The

corresponding scan line is presented in figure 7.8.

Figure 7.8 The scan line including the borders (A&B) of the thyroid nodule.

Chapter 7

79

Figure 7.9 Scan profiles of US thyroid image. High intensity line corresponds to the denoised

scan line whereas low intensity line to original image. (a) ASSF method, (b) Soft

thresholding, (c) hard thresholding, (d) wavelet inter-scale analysis denoising

The performance of the proposed method on various US images is depicted in figures 7.10,

7.11, 7.12.


80

(a) (b)

Figure 7.10 (a) Original US image, (b) De-speckled US image

(a) (b)

Figure 7.11 (a) Original US image, (b) De-speckled US image

(a) (b) Figure 7.12 (a) Original US image, (b) De-speckled US image

Chapter 7

81

7.3.3 Observer Evaluation Study

Sixty three US images of the thyroid gland were included in a questionnaire (Figure 7.13) that

comprised seven queries concerning various visual observations regarding the proposed

algorithm’s effectiveness.

Figure 7.13 Microsoft access interface employing the questionnaire for US images denoising

evaluation

The image dataset was acquired following the same parameter’s protocol in the time interval

from October 2003 to September 2004. The questionnaire was implemented in Microsoft

Access. The seven queries were:

1) Removal of speckle – granular pattern.

2) Improvement of micro-calcification detection inside the thyroid nodule.

3) Creation during denoising of artefacts and ghost images.

4) Preservation of nodules boundaries, resolvable details and anatomical structures.

5) Contrast enhancement between nodule and surrounding environment.

6) Revealing of small structures invisible in the original image.

7) Improvement of diagnostic evaluation procedure.

The study was performed by two experienced qualified radiologists specialized in

ultrasonography. The reviewing of all cases was done independently on a high resolution

monitor. The ranking for each query ranged from 0 to 100 with a 25-point step corresponding

to fail (0), poor, good, very good and excellent performance (100), except query number 3

where low score refers to high effectiveness (Tables 7.3 and 7.4). The performance of the


82

proposed method, based on both observers evaluation, was assessed by means of the

percentage of cases where the algorithm is effective (>=50) in all queries (Table 7.5). Inter -

observer agreement was determined using the weighted K (kappa) coefficient calculated for

all qualitative parameters [117]. A kappa statistic above 0.75 was arbitrarily chosen so as to

show excellent agreement, between 0.40 and 0.75 as moderate agreement and below 0.40 as

poor agreement – Table 7.6.

Table 7.3 1st Observer’s evaluation of algorithm performance

QUERIES Number of US images 1 2 3 4 5 6 7

1 50 100 75 25 100 0 75

2 25 100 75 50 100 0 100

3 25 50 50 25 50 0 75

4 75 75 75 25 100 0 100

5 25 100 50 25 100 0 75

6 50 50 50 25 25 0 50

7 75 50 50 75 100 0 100

8 0 100 100 100 100 0 100

9 0 100 100 0 100 0 100

10 50 100 75 50 100 0 100

11 0 75 50 25 50 0 75

12 100 50 75 0 50 0 75

13 75 100 100 50 100 0 100

14 50 75 50 0 100 0 50

15 0 25 25 75 50 0 50

16 25 75 75 0 75 0 75

17 75 100 100 0 100 0 100

18 50 75 50 0 75 0 50

19 0 100 100 0 100 0 75

20 0 25 25 0 25 0 50

21 0 75 75 0 100 0 100

22 0 50 50 0 75 0 75

23 75 25 50 0 25 0 75

24 0 75 75 0 75 0 75

25 0 75 75 0 75 0 75

26 75 100 100 0 100 0 75

27 0 50 50 0 75 0 75

28 0 25 25 0 25 0 50

29 0 50 50 0 50 0 50

30 0 25 25 0 25 0 25

31 100 75 100 0 75 0 100

32 75 75 50 75 75 0 75

33 0 75 75 50 75 0 75

34 0 50 50 0 25 0 50

35 0 25 25 0 25 0 50

36 75 75 75 0 75 0 75

37 0 25 25 0 25 0 25

Chapter 7

83

38 50 50 50 0 50 0 50

39 0 25 25 0 25 0 25

40 75 75 75 0 75 0 75

41 75 75 75 0 50 0 75

42 0 75 75 0 75 0 75

43 0 25 25 0 25 0 50

44 50 25 50 0 25 0 50

45 0 75 50 100 75 0 100

46 0 75 75 0 75 0 75

47 0 25 25 0 25 0 50

48 50 75 75 0 75 0 75

49 0 50 50 0 50 0 50

50 0 50 50 0 50 0 50

51 75 75 75 0 75 0 75

52 0 50 25 0 50 0 50

53 75 25 50 0 50 0 75

54 50 50 50 0 50 0 50

55 0 50 50 0 75 0 75

56 0 75 75 0 75 0 75

57 0 25 25 0 50 0 50

58 0 50 25 0 25 0 50

59 0 50 50 0 50 0 50

60 75 100 100 0 100 0 100

61 0 50 50 0 50 0 50

Table 7.4 2nd Observer’s evaluation of algorithm performance

QUERIES Number of US images 1 2 3 4 5 6 7

1 75 75 75 0 100 0 100

2 0 100 100 0 100 0 100

3 0 25 25 0 25 0 50

4 25 75 75 0 75 0 75

5 50 75 75 0 100 0 100

6 100 50 75 0 25 0 75

7 100 75 75 0 75 0 75

8 0 75 75 100 75 0 75

9 0 75 75 0 75 0 100

10 0 75 75 0 100 0 75

11 0 75 75 0 75 0 75

12 100 50 75 100 25 0 75

13 100 75 100 100 75 0 100

14 75 100 75 0 100 0 75

15 0 50 50 75 50 0 25

16 50 75 75 0 100 0 75

17 75 100 100 0 100 0 100

18 0 25 25 0 25 0 75

19 0 100 100 100 100 0 100

20 0 25 50 0 50 0 50

21 0 100 100 0 100 0 100

22 0 100 100 0 100 0 100


84

23 100 50 100 100 50 0 100

24 0 100 100 0 100 0 100

25 0 100 100 0 100 0 100

26 100 100 100 0 100 0 100

27 0 50 25 0 50 0 50

28 0 25 25 0 25 0 25

29 0 25 50 0 50 0 50

30 0 25 25 0 25 0 50

31 100 75 100 50 75 0 100

32 75 75 100 100 75 0 75

33 0 100 75 0 50 0 75

34 0 75 75 0 25 0 100

35 0 50 25 0 50 0 75

36 100 100 100 75 100 0 100

37 0 25 25 0 25 0 50

38 75 100 100 75 100 0 100

39 0 25 25 0 25 0 50

40 50 100 100 75 100 0 100

41 50 75 75 75 75 0 100

42 0 50 50 0 50 0 75

43 50 50 50 0 25 0 50

44 75 50 75 0 25 0 75

45 0 100 50 100 100 0 100

46 75 75 50 0 75 0 75

47 0 25 25 0 25 0 25

48 0 75 100 0 75 0 100

49 0 25 25 0 25 0 50

50 0 50 50 0 50 0 50

51 50 75 75 0 50 0 75

52 0 50 50 0 50 0 75

53 50 50 50 0 50 0 50

54 0 25 25 0 25 0 50

55 0 50 50 0 50 0 75

56 25 50 50 0 50 0 75

57 0 25 25 0 25 0 50

58 50 25 25 0 25 0 50

59 0 25 25 0 25 0 50

60 75 100 100 0 100 0 100

61 0 25 25 0 50 0 25

Table 7.5 Observers evaluation of algorithm performance

Observer A Observer B

Ranking >=50 <50 Efficiency Percentage

>=50 <50 Efficiency Percentage

Query 1 55 8 87 % 55 8 87 %

Query 2 28 35 44 % 27 36 42 %

Query 4 46 17 73 % 50 13 79 %

Query 5 48 15 76 % 49 14 78 %

Chapter 7

85

Query 6 50 13 79 % 51 12 80 %

Query 7 14 49 22 % 14 49 22 %

Table 7.6 Agreement (kappa coefficient) between the two observers

Kappa Coefficient

Query 1 0.86

Query 2 0.71

Query 4 0.56

Query 5 0.54

Query 6 0.55

Query 7 0.67

7.4 Discussion and Conclusions

Multiscale wavelet analysis is one of the most promising approaches for speckle suppression

in ultrasound imaging. The proposed method attempts an optimal speckle reduction in US

images of the thyroid gland, employing singularity detection on local maxima chains within a

coarse to fine framework. Significant image features are represented across scales with

maxima chains of positive Lipschitz regularity while speckle noise gives rise to maxima

chains of negative Lipschitz regularity. The combination of the proposed back-propagation

maxima tracking together with the singularity detection achieved high speckle reduction

performance with remarkable edge preservation accuracy.

An important task of any multi-resolution algorithm is to optimize the detection of high

resolution information. The back-propagation approach through the position-angle pair and

occasionally amplitude, together with the adaptive neighbourhood size, approximates with

significant proximity the coarse information even at the 21 scale (see Figure 7.5). Nevertheless

the implementation of an optimized coarse to fine connection is still under investigation. Any

prior information regarding potential patterns within the US image can be utilized in this

research. The method is generic and can be also applied to US medical images of different

anatomical structures along with other imaging modalities suffering from the presence of

speckle such as synthetic aperture radar images.

The comparative study regarding the effectiveness of all methods was based on their speckle

reduction and edge preservation properties. Regarding speckle reduction on the phantom

image, both SI and S/mse obtained from the inter-scale analysis method were greater

compared with the equivalents of the other three methods locally and totally on the phantom

image (Table 7.1). Accordingly, regarding parameter β, the proposed algorithm exhibited

greater performance.


86

The results of the proposed method on the thyroid US image (SI, S/mse and β) exhibited much

greater scores than the other three methods (Table 7.2). Additionally, a closer look in figure

7.9(d) can help us observe that the inter-scale wavelet denoising method retained the

boundaries of the thyroid nodule, similar to that of the original image, while at the same time

the speckle suppression degree in speckle regions was high. An interesting observation made

from the same figure was the tendency of Karaman’s and Donoho’s soft thresholding methods

to remove completely the signal fluctuation in a homogeneous regions, thus eliminating

possible small low contrast structures while failing to follow with a relative compliance the

initial trend. At the same figure the spurious oscillations resulted from Donoho’s hard

thresholding method are also apparent.

The results of the questionnaire given in the two specialized doctors can give us some useful

conclusions regarding the adaptability and power of our method. The scores in queries 1 and 4

(>70% evaluation efficiency percentage of both observers) confirmed the results the

algorithm had in speckle reduction and edge preservation. High score in query number 5

(>75% evaluation efficiency percentage of both observers) proved that a successful noise

suppression without the creation of blurring actually increases the contrast of various

structures in regard with the surrounding environment. An important subject introduced in

this study through query number 6 (>75% evaluation efficiency percentage of both observers)

is the potential of the algorithm to reveal structures that are not easily distinguishable by the

human eye.

The low score in query number 7 is predictable due to the great expertise of both observers

regarding the final diagnosis. However in less experienced physicians it could turn out as a

very useful tool. The correlation results between the two observers are indicative of the

algorithm’s ability. Particular attention should be given to the high correlation (k=0.86) of the

two observers regarding the speckle suppression efficiency of our method, constituting an

additional advantage of the proposed algorithm.

As a final conclusion we can say that an efficient wavelet-based speckle reduction is

presented in this article. This method was based on inter-scale wavelet analysis, in which the

primal aim was to isolate edges existing across scales and check their regularity. Successful

speckle suppression made by the proposed algorithm can be employed as an additional step in

the improvement of the overall diagnostic procedure.

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CHAPTER 8

Thyroid Nodule Boundary Detection in Ultrasound Images

Summary

In this chapter a multiscale hybrid model is introduced for unsupervised thyroid nodules

boundary extraction from US images. The chapter is organized as follows: At first an

extensive review of the literature regarding segmentation in US images is presented. In the

Materials & Method section, the speckle reduction – edge detection proposed strategy, the

introduced multi-scale structure model and the constrained Hough transform are presented. In

the Results section, the performance of the hybrid method applied on real US images is

demonstrated. In addition, an inter-observer study was carried out between the two physicians

to estimate the degree of variance the manually boundaries present. In the last section an

extensive review and discussion regarding methodology, performance and potentials of the

algorithm are given.


Numerous computerized segmentation methods have been employed in US imaging of the

prostate, kidney, cardiac anatomy, ovaries, fetal head and breast lesions. All these algorithms

can be categorized in five types depending on the strategy chosen for segmenting the ROI.

Segmentation methods based on (a) edge detection [118-123], (b) texture or feature analysis

[124-130], (c) deformable and active models [131-141], (d) methods based on multiscale

algorithms that visualise US images at different level of resolution [142-145] and (e) methods

based on combination of the above algorithms for optimization of the results [146-159]. An

overview is presented below of segmentation algorithms applied in US imaging.

An edge-based segmentation algorithm detects any abrupt changes in gray level values within

the US image. For the final contour extraction an additional process is performed to select and

link edge pixels. Various edge detection methods for segmentation of US images have been

developed throughout the past decade. Kwoh et al [118], in order to avoid false edges and

broken segments created by the radial bas-relief (RBR) method, applied the Fourier transform

related harmonic method directly in the skeletonized edge image to extract the final prostate

smooth contour. Aarnink et al [119] implemented a pre-processing algorithm for US image

segmentation in which edges were detected with a non-linear Laplacian operator based on the

detection of zero crossings. Aarnink et al [120], also proposed a post-processing algorithm

applied in the edge map, obtained from zero crossing detection, in which he integrated edge

maps for outlining the region of interest. Sarty et al [121] introduced a complex semi-

Thyroid Nodule Boundary Detection in ultrasound images

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automatic algorithm for segmentation of ovarian follicular US images. It was based on a user

defined ROI’s edge strength and direction for approximate inner wall border detection.

Subsequently, the prior knowledge of follicles inner and outer wall border intensity profile

was employed for outer wall contour delineation. Pathak et al [122], applied a speckle

reduction – edge enhancing technique called ‘sticks’ as well as anisotropic diffusion filtering

combined with shape prior knowledge for differentiation of prostate’s from false edges. Yu et

al [123] used the instantaneous coefficient of variation detector which combined gray level

intensity profile with first and second derivative operators for edge detection in ultrasound

images.

In texture analysis, rather than trying to locate edges in a US image, several texture features

are employed for region characterization. These features usually serve as input to a

classification or clustering algorithm to discriminate a group of pixels as correct or false

regions. Richard and Keen, 1996 [124] used a pixel-classifier based on four feature images

resulting by energy measures associated with each pixel. A clustering algorithm is employed

for each pixel to discriminate the most probable class to achieve prostate segmentation.

Zimmer et al [125] implemented a minimum cross entropy thresholding algorithm employing

a linear combination of gray level and local entropy values for segmenting US images of

ovarian cysts containing fluid and surrounded by soft tissue. Potocnik et al [126] combined

the detection of homogenous regions, derived from gray-scale histogram, within the ovarian

US image and a region growing algorithm that employs a centre to contour filling until the

borders of the growing object meet with the ovary’s contour. Docour and Olmez [127] used a

hybrid neural network having as input textural feature data obtained from discrete cosine

transform of pixel intensities in ROI’s for segmentation of US images of several anatomical

structures.

Huang and Chen [128] utilised textural analysis as input to a self organised Neural Network

classifier. After the classification of the textural features, a watershed segmentation algorithm

determined the final contour of breast tumours. Archip et al [129] introduced a US imaging

segmentation method that uses unsupervised spectral clustering subsequent to anisotropic

diffusion filtering. Strzelecki et al [130] employed texture features as input to an oscillating

neural network, based on the ‘temporary correlation’ theory, to segment intra-cardiac masses

from cardiac tumour echocardiograms.

Model – based segmentation approaches use either a priori knowledge with well-known

active contours and deformable models, or statistical models without the use of any prior

information regarding the ROI. Lorenz et al [131] applied a two folded probabilistic method

by means of the assumption that the contour sequence is a two-dimensional first order

Markov random process and the prior knowledge about the prostate’s contour shape. The

contour estimation was performed using iteratively the maximum a posteriori principle.

Chapter 8

- 89 -

Pathak et al [132] introduced an automatic algorithm for inner and outer scull boundaries

detection of foetal head in US images. The algorithm has as input a user defined centre of the

foetal head and generates an initial contour. That contour is fed in an active contour model

that assumes that the desired boundaries lie along high gradient points for detection of the

inner scull boundary. This boundary in complement with a priori shape knowledge (ellipse) is

passed into the active contour model to outline the external scull boundary. Obadia et al [133]

developed a semi-automatic snake-based approach incorporating local statistics boundary

models (gradient, 1st and 2nd order statistics) along with on the fly training of the boundary

models for US image segmentation. Ladak et al [134] developed a semi-automatic method

based on a deformable contour model, named the discrete dynamic contour. An initial contour

was outlined via cubic interpolation functions arising by four manually selected input points.

The deformable model following utilizes gradient direction information to estimate the final

contour. Chen et al [135] combined a distance map computed by the early vision model and

investigation of snake elements derived from a discrete-snake model for a semi automatic US

image segmentation. Chen et al [136] also proposed a snake model for segmentation of

sonographic images in which he compound the modified trimmed mean filter for speckle

suppression, the ramp integration for weak edge enhancement for detecting edges and the

adaptive weighting parameters for fine tuning of the deformation process. Wu et al [137]

developed a feature model-based boundary recognition method combining prior information

about the prostate such as shape and size, and a genetic algorithm for object boundary

detection with model constrains. Chen et al [138] also proposed a dual snake deformable

model for boundary extraction from US images. It is a combinative study that comprised a

new external force called discrete gradient flow, a new edge strength weighting scheme and a

new stability index for the two underlying snakes. Sandra et al [139] applied a region-based

model to derive the likelihood estimation function via low order parameterization of the

contour shapes to extract anatomical structures from foetal ultrasound images. Cvancarova et

al [140] via some snake algorithms and a modification of the well known gradient vector flow

model they segmented liver tumors from US images. Rabhi et al [141] proposed a geodesic

active region model, based on boundary and region information, for segmentation of

thrombosis in vivo venous ultrasound images.

Multiscale methods decompose the input US image into several different levels of resolution

in order to acquire all available information towards an efficient segmentation. Lain and Zong

[142] utilised wavelet multiscale analysis combined with shape-matched filtering to estimate

the center point of the LV. Consequently, a boundary contour reconstruction process is

employed to link the cardiac broken segments and finally a filtering process of the closed

boundary to extract the ROI. Liu et al [143] used the RBR method for edge enhancing and a

multi-resolution analysis to obtain a skeletonized image, which was superimposed on the


- 90 -

original US image of the prostate as an edge map. Lin et al [144] employed a combinative

multiscale framework for echocardiographic image segmentation. At the coarse scale a

temporary boundary was computed based on region homogeneity and edge features. A coarse

to fine boundary evolution was then employed, based on shape similarity constraints, for

contour refinement. Davignon et al [145] performed a multi-parametric approach for the

segmentation of ultrasonic data. Various maps of local features, derived from statistical

measurements using a Bayesian multi-resolution Markov random field, were used for a pixel-

based tissue differentiation.

Most contemporary algorithms use combinative strategies in order to overcome the

difficulties arising from the nature of US imaging. Boukerroui et al [146] employed various

textural features (uniform or slowly varying intensities versus sharp transitions) obtained from

a wavelet wavelet-based multi-resolution pyramid in a K-mean clustering algorithm for

automatic extraction of breast tumors. Chen et al [147] proposed a novel texture edge

detection method in US imaging in which edges are the local maxima of a weighted distance

map based on an early vision model. Prior the built of the texture edge map, the US image is

undergone a texture enhancement procedure employing multi-scale wavelet analysis.

Mignotte et al [148] implemented an optimization approach for segmentation of endocardial

contour and inner wall of arteries from US imaging. An initial snake position is derived from

active contour model and gray level statistical information obtained bilaterally of the objects

boundary. The final contour is outlined within a multi-scale framework for minimization of

the initial snake’s global energy function. Boukerroui et al [149], via a wavelet multi-

resolution analysis and the use of a weighting function on both local and global statistics

achieved to segment breast and echocardiographic sequences ultrasound data. Kotropoulos

and Pittas [150] applied Support Vector Machines as a classification tool to differentiate

lesions from background in a US image. The authors used a running window over the US

image and divided each of the regions as positive and negative pattern according their gray

level histogram.

Chin et al [151] introduced a semi-automatic segmentation in US images. It is based in initial

contour tracking derived from wavelet coefficients calculated from Dyadic Wavelet

Transform and in the Discrete Dynamic Contour deformation model for the final contour

estimation. Xie et al [152] proposed a supervised segmentation method in which a texture

model and a shape prior model were combined to partition the US image in two regions,

inside and outside the contour curve of kidneys. Flores et al [153] introduced a segmentation

algorithm for breast tumours. The segmentation approach, originally estimated an initial

snake through a region growing method based on gradient information. Then it served as

input in an active contour model for the final extraction of the tumour. Betrouni et al [154] in

his attempt to segment the prostate from trans-abdominal US images reduced speckle with an

Chapter 8

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adaptive noise filter as a pre-processing step. Afterwards, he applied a statistical prostate

model, based on heuristic searches, to the final contour. Dydenco et al [155] used a level set

representation, that incorporates both shape and motion prior knowledge, for segmentation

and region tracking in echocardiographic sequences. Liu et al [156] combined a multi-

resolution approach for active contour initialization and the Gradient Vector Flow (GVF)

model. The GVF model uses prior shape knowledge for segmenting thermal lesions in

elastographic US images. Fernadez and Lopez [157] applied a delineation algorithm on a

sequence of kidney US images within a Bayesian framework with two components: a

Marcom Random Field with an active contour model based on star-like shape prior

knowledge for initial detection, and a likelihood model having as input both intensity and

gradient information for the final and correct contour estimation. Eslami et al [158] combined

a Gibbs joint probability function for image transformation, wavelet transform for initial

contour estimation and finally an active contour model for lesion detection in kidney

ultrasonic images. Gong et al [159] described a deformation-based method incorporating prior

shape knowledge (the ROI is modelled as super-ellipse) and parametric deformations for

automatic segmentation of prostate ultrasound images.

The poor US image quality in general, in conjunction with the drawbacks arising from the

nature of ultrasound, limit the performance of various segmentation methods, proposed

throughout the past decade. Most edge based techniques generally detect changes in the grey

level profile and usually are unable to isolate and extract the ROI. Segmentation approaches

based in textural characteristics are optimised for particular US images and suffer from the

presence of adjacent tissues that exhibit similar acoustic properties. More complicated

algorithms, based on active models or multi-scale analysis, are usually semiautomatic.

Moreover, the lack of detailed information regarding the way authors handle the presence of

adjacent structures is worth noticing.

Many researchers in their attempt to overcome some of these limitations convert their

methods into semi-automatic, thus transformed them into user-dependent approaches. Others

incorporated prior knowledge information regarding shape or texture features in order to

optimize their results. Besides the difficulties most segmentation algorithms encounter, US

imaging of thyroid nodules carry additional disadvantages. Thyroid nodules lack of uniform

echogenicity behavior (i.e nodules can be hypo-, iso- or hyper-echogenic in regard with the

surrounding tissue), which in turn means that no prior information regarding texture

characteristics can be employed to enhance the algorithm’s efficiency for all cases. Most

proposed methods attempt to calculate a closed contour as a final segmentation outcome.

Again in thyroid US imaging, the presence of diffusion between the nodule and the

surrounding tissue is of importance clinical information for the physician, thus any algorithm

that approximate a closed contour might mislead the physician.


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8.2.1 Overview and Implementation of the Algorithm

In the proposed method a multiscale hybrid model is introduced for unsupervised thyroid

nodules boundary extraction from US images. Our approach, in order to overcome the texture

limitations in US thyroid imaging, integrates a wavelet-based multiscale edge detection into

an across scale structure detection model for a contour map estimation. The final contour

map, derived from the introduced model, serves as input to a constrained Hough transform for

nodule detection. The Hough transform is invariant to any open contours which may be

derived from the multiscale structure model. A schematic representation of the algorithm’s

steps is depicted in Figure 8.1. At first, a speckle reduction – edge detection procedure is

implemented based on a multi-fold wavelet-based analysis. A wavelet decomposition at four

dyadic scales with the "á trous" algorithm is employed, in which speckle is removed via a

coarse to fine analysis of Wavelet Transform Modulus Maxima (WTMM). The back-

propagating local maxima with positive Lipschitz exponents ‘a’ are considered of value and

utilised in the subsequent multiscale structure model. On the other hand, back-propagating

local maxima with negative Lipschitz exponents are classified as speckle and discarded.

A multi-scale pixel representation is derived from the speckle removal – edge detection

procedure, in which pixels of the input US image are associated with WTMM. A further step

of this method is to consider a multi-scale structure representation which would associate an

anatomical object in the image with a volume in the multi-scale edge transform. A multi-scale

structure model has been developed for boundary detection in US images. The principal

components of the introduced model are the WTMM, the Maxima Chains which are groups of

local maxima with similar properties at the same scale, the Structures which are a set of

connected maxima chains, the Interscale relation which determines the criteria employed for

the algorithm to relate maxima chains across scales into a significant structure and the

Structure Operator that indicates in which structure a given maxima chain belongs to.

All mentioned components are integrated to form a multi-scale contour representation. In

order to extract the nodule’s boundary, the last scale of the contour decomposition is

employed as input into the constrained Hough transform based in ‘a priori’ shape knowledge

for partial circular object recognition.

The software development of the proposed method and the user-friendly software for manual

delineation from the two observers was implemented with Matlab 6.5. The computer used for

processing has an AMD Athlon XP+ processor running at 1.8 GHz and 512 of RAM.

Chapter 8

- 93 -

Figure 8.1 Schematic representation of the segmentation algorithm.


- 94 -

8.2.2 US Data Acquisition

All US images used throughout this study were obtained from an HDI-3000 ATL digital

ultrasound system – Philips Ultrasound P.O. Box 3003 Bothel, WA 98041-3003, USA – with

a broadband (5-12 MHz frequency band) linear array. The sonographic scans were taken in

both the transverse and longitudinal plane and instrument settings were set accordingly to the

built-in ‘SmallPartTest’ Philips protocol. The selected static US frames were digitized by a

video card “frame grabber” (Miro PCTV, Pinnacle Systems) installed in a PC, capable of

acquiring and displaying US images with a 768 x 576 resolution at 8 bits.

8.2.3 Edge Detection Procedure

8.2.3.1 Multiscale Edge Representation

Multiscale Edge Representation (MER) utilizes the local maxima of the Dyadic Wavelet

Transform (DWT) for characterization of signals from multi-scale edges. MER can be

considered as a transformation from the initial US image representation into a feature

representation based on the image’s intensity sharp variations defined as edges [62]. This

transformation is considered as an intermediate step for analysis towards thyroid nodule

segmentation. The proposed method decomposes the multiplicative speckle model into an

additive signal dependent noise model, which in turn means that it omits the log-transform to

avoid the mean bias correction problem [108, 109]. The two-dimensional DWT is the set of

functions )),(),,(( 22

12

yxfWyxfW jj and is given by:

( )( )

( )( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∗∂∂

∗∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛∗=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

yxfy

yxfxf

yxfWyxfW

j

j

j

j

j

j j

,

,2

),(),(

2

2

22

12

2

1

2

2

θ

θ

ψψ

8.1

Where ),(1 yxψ and ),(2 yxψ are the analyzing wavelets, ),( yxθ is a symmetrical

smoothing function approximating the Gaussian, f is the image function )(),( 22 RLyxf ∈ and

j the dyadic scale. The two-dimensional wavelet transform of an image can be viewed as a

gradient vector (Equation 8.2) whose magnitude and phase are given by Equations 8.3 & 8.4.

),)(*(2),(),(

22

1

2

2 yxfyxfWyxfW

j

j

j j θ→

∇⋅=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ 8.2

22

222

12

),(),(),( yxfWyxfWyxfM jjj += 8.3

Chapter 8

- 95 -

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

),(),(

tan),( 12

221

2 yxfWyxfW

yxfAj

j

j 8.4

8.2.3.2 Coarse to Fine Analysis

The next step afterwards MER is a coarse to fine procedure that employed all available

information of WTMM at different frequency bands for pointwise singularity detection.

Lipschitz regularity was the main criterion towards classification of edges as speckle or

important sharp variations. The outcome of this procedure was a multi-scale edge map that

relates all significant information of the US image with WTMM. The discrimination between

edges that correspond to structures and those arising from speckle or artifacts was a two-

folded process. At first, groups of maxima that back-propagate from coarse to fine scales were

detected and formed vectors in the scale-space plane, and afterwards were utilized for

singularity detection via the Lipschitz exponents – a – [68,70].

That inter-scale information is acquired by means of a back-propagation connectivity of the

wavelet transform modulus maxima. The grouping of local maxima across scales is made on

the basis that if an edge exists in a coarser scale, it can also be located in all available finer

scales [70]. Two local maxima from two successive scales are grouped together if they

possess a close position in the image plane and similar angle value. This back-propagation

tracking, from the coarsest scale 2j to the finer scale 21, produces curves of maxima in the

scale-space plane (termed as maxima lines – ML), which take the following form:

⎭⎬⎫

⎩⎨⎧

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡= −−− 111111 2

,2

,2

,...,2

,2

,2

,2

,2

,2

PAMPAMPAMML jjjjjjk 8.5

where: M, A and P are the magnitude, angle and position of each local maximum at a given

scale and k the total number of local maxima found in the coarsest scale 2j where the back-

propagation tracking is employed.

The magnitude parameter is exploited in cases where a coarse local maximum is computed to

back-propagate in more than one finer local maxima. In such cases the maximum with the

greater magnitude is chosen to form the maxima line. The coarse to fine local maxima

detection is made with a corresponding large to small investigation window, depending on the

length of the dilated filter for each scale. In coarse scales the window is relatively the same

with the corresponding dilated filter with 2j-1 inserted zeros while in the finer scale available

the window has the same size as the filter without dilation.

The decay of log2|Mf(2j,x,y)| as a function of log2s is estimated along all maxima lines that

correspond to singularities with varying Lipschitz regularity. When the maxima amplitude

within the maxima line decreases when the scale decreases its Lipschitz regularity is positive


- 96 -

(positive Lipschitz exponents). On the contrary, in a maxima line with maxima amplitudes

that increase when the scale decreases the Lipschtiz regularity is negative (negative Lipschitz

exponents). The local maxima being part of maxima lines with positive Lipschitz exponents

correspond to important edges, whereas local maxima inside maxima lines with negative

Lipschitz exponents correspond to speckle. After the coarse to fine analysis the back-

propagating maxima with positive Lipschitz regularity are utilized as input to the subsequent

multi-scale structure model.

The implementation of the MER requires the computation of the wavelet transform for scales

21 to 2N. The choice of the parameter N depends on the application. For feature extraction and

segmentation methods the choice of N is crucial. The Lipschitz regularity calculation of two

adjacent singularities, considers as prerequisite that the two sharp variations are isolated. As

the dilation of the wavelets and the smoothing function are increased, the resulting

singularities will begin to overlap. In order to estimate the optimum dyadic level, the location

of each sharp variation is associated with the WTMM. In this study, it is experimentally

shown that the localization of WTMM is increased from N=1 to N=4. From this scale and on,

the evolution of WTMM across scales produce localization and numerical errors. In fact, the

majority of local maxima tracked at scale N=4 are converged into a single maxima at N=5

whereas a small fraction demonstrates irregular behavior, which in turn produces negative

Lipschitz exponents between these two scales.

8.2.4 Multi-Scale Structure Model

The proposed structure model considers a significant structure as a hierarchical set of

connected maxima chains. A structure representation is obtained, in which structures are

bridged maxima chains with similar properties across all available scales. The fundamental

parameters that the introduced model employs to generate the multi-scale structure

representation, are presented below:

- Local maxima: the back-propagating WTMM derived from the speckle reduction – edge

detection step.

- Maxima Chains: WTMM are grouped together in each available scale with similar

properties forming one-dimensional curves, termed as maxima chains (Figure 8.2). A chain

(C) is a set of linked local maxima at a given scale 2j:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡= ),(j2

M,...,),(j2M,),(j2

Mk,j2

C 2211 pp yxfyxfyxf 8.6

where M is the amplitude, k and p the number of chains and local maxima included in the

chain respectively.

Chapter 8

- 97 -

Figure 8.2 Local maxima linking procedure. Adjacent local maxima form a maxima chain

kjC ,2 due to positional proximity combined with amplitude and angle values similarity.

- Structures: a structure is a set of connected maxima chains at the same scale. A significant

structure derived from adjacent chains is of the form:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

ijCjCjCjS,2

,...,2,2

,1,22

8.7

where i is the number of adjacent maxima chains bridged to form a structure and j2 the

coarsest scale.

- Inter-scale relation: the criteria employed for the algorithm to relate maxima chains across

scales into a single structure.

- Structure operator: which indicates to which structure a given maxima chain belongs to.

8.2.4.1 Maxima Linking

The previous edge detection procedure generated a speckle-free multi-scale pixel

representation, where each pixel corresponds to WTMM emanating from various structures

located within the US image. Nevertheless, individual wavelet maxima are mostly not

independent features; they are part of certain lines or curves localized in multiple scales. The

initialization of the model is implemented as global searching of WTMM in each scale with

matching properties. The maxima chain linking procedure creates curves comprising of local

maxima groups at each scale. The connectivity procedure is a complicated operation

depended on directional compatibility, spatial adjacency and amplitude similarity. The latter

can be rephrased as two edge-points in a given scale, linked to form a maxima chain on

condition that they are close to each other and have similar phase and amplitude values.


- 98 -

8.2.4.2 Structure Identification

Despite the chaining procedure, small gaps between adjacent maxima chains are created

resulting to a broken outline. The main reasons of this inadequacy are: possible transducer

displacement from the physician during US examination, various acoustic phenomena such as

refraction, shadowing and reverberation, and numerical errors made during the calculation of

the coarse to fine evolution of WTMM. These numerical errors are caused by the fact that the

wavelets used (quadratic spline) are not the derivative of a Gaussian but only an

approximation. An efficient structure representation prerequisites continuity of chains.

The rule applied to connect two maxima chains into a single structure is termed as ‘inter-scale

relation’. All maxima chains located in the multi-scale edge map correspond to significant

segments of a broken borderline. Each of the maxima chains is approximated by its mean and

position. This approximation of a maxima chain is expressed by the following equation:

[ ]⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=∑

p

p

p

jj

jjj

j PPp

MMMC

,21,21

,22,21,2

2,,

),...,,( 8.8

where j

2 is the dyadic scale, M2j,1..:p are the amplitude values of the chain, p the number of

local maxima and pjj PP

,21,2, are the chain’s maxima starting and ending positions. Two

maxima chains at two successive scales jC2 – 12 +jC are said to belong to a single structure

because of their maxima positions proximity. This means that the majority of the local

maxima compose a maxima chain jC2 must also be contained in the maxima chain 12 +jC .

Moreover, two adjacent maxima chains at a given scale comprise a single structure due to

position and mean-amplitude similarity.

All maxima chains, appearing in successive scales that satisfy the above two rules are

connected in such a way to form a structure. In each structure defined as a set of maxima

chains, an operator L is assigned which indicates the arithmetic label given at each detected

group of connected maxima chains: li

CL j =),2

( , where i is the number of maxima chains

and l is the arithmetic label of each structure. In the resultant structure representation any

individual maximum that is not linked during the chaining is removed. Once the structure

representation has been implemented the structure image from the coarsest scale is

transformed into a Boolean one (i.e. pixel intensity equals 1 when a maximum is detected and

zero otherwise). An additional step is required to separate and detect the important structure

that corresponds to the thyroid nodule from other various structures that correspond to

Chapter 8

- 99 -

different anatomical regions located in the US image. A pseudo code of the structure

detection procedure that constructs the multiscale structure representation is depicted below.

PSEUDO CODE

8.2.5 Nodule’s Boundary Extraction

The boundaries of several anatomical parts investigated in medical imaging such as

kidney, prostate, parts of the heart and of course thyroid nodules can be approximated by

regular curves. As already stated in the introduction section, despite the irregularity degree of

its contour, every thyroid nodule retains a partial circular shape [1-46]. The edge detection

methods do not extract the ROI. In optimal algorithm performance, the candidate anatomical

structure is revealed noise-free in the xy-plane surrounded by other anatomical structures

present in the medical image. An efficient technique to isolate features of a particular shape

within an image is the Hough transform. The classical Hough transform requires that the

desired features must be specified in some parametric forms, by regular curves such as lines,

function STRUCTURE DETECTION returns multiscale structure representation

⁄⁄ maxima chain construction

inputs: N =4, the maximum decomposition scale.

Multi-scale Edge Map with⎟⎟⎠

⎞⎜⎜⎝

⎛),(

2yxfjM 41 ≤≤ j ←local maxima classified as important edges

for each scale: 2j (j=1←N) do

find ⎟⎟⎠

⎞⎜⎜⎝

⎛),(

2yxfjM with similar position, amplitude and phase values,

construct maxima chain: jC2

←⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

PjMjMjM,2

,...,2,2

,1,2

⁄⁄ structure detection

for each NC2

do

for all finer scales: 21 ← 23 do

if there are maxima chains⎟⎟⎠

⎞⎜⎜⎝

⎛12

,22,32

CCC with similar position values

construct unified maxima chain across scales: 12 ≤≤ jN

jC ←⎥⎥⎦

⎤

⎢⎢⎣

⎡∪ = jCN

j2

1

and if two adjacent maxima chains1

)2,2

(),1,2

(≤≤⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

jNjCjC with position and amplitude proximity

assign structure operator: L← ),2

(ijCL , i←number of connected maxima chains in each scale

construct structure ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡←

ijCjCjCjS,2

,...,2,2

,1,22


- 100 -

circles, ellipses, etc. [160] whereas the generalized Hough transform can be employed in

applications where a simple analytic description of a feature is not possible [161]. Due to the

computational complexity of the generalized Hough algorithm, we have restricted our

boundary extraction attempt within the framework of the classical Hough transform.

8.2.6 Constrained Hough Transform

The main idea of the Hough transform can be considered as a point to curve transformation

from a Cartesian image space map in the Hough parameter space. When viewed in Hough

parameter space, points that are collinear in the Cartesian image space become readily

apparent as they yield curves, which intersect at a common point. From the synthetic image of

Figure 8.3 (a), a Boolean map is derived with labeled structures corresponding to several

anatomical regions.

For every structure a reference point (xref,yref) is computed based on the x and y coordinates

of the maxima constituting each structure. Each reference point is considered as candidate

center-point for a circular object with a varying radius ri:

( ) ( )222:1 refirefipi yyxxr −+−== 8.9

where xi, yi are the coordinates and p the number of the connected maxima for each

structure.

Circles are projected around the candidate center-point, and for each maxima point on the

structure boundary, the corresponding cell in the accumulator array is incremented by one.

The accumulator matrix representing the Hough parameter space has the same dimensions as

the original, and the method involves projecting circles using Cartesian coordinates (Figure

8.3 (b)).

8.2.7 Accumulator Local Maxima Detection

As a result in the parameter space those reference points located within circular objects (i.e.

thyroid nodule) are related with relatively large values in the accumulator array, in contrast to

other structures (i.e. veins, arteries …etc). In Figure 8.3 (c) we can observe that the cell

approximately corresponding to the simulated nodule’s center appears as the maximum value

in the parameter space. A local maxima detection procedure is applied in the accumulator

array to find the approximate center. Subsequently, its corresponding structure is

superimposed on the image as the final segmentation outcome (Figure 8.3 (d)).

Chapter 8

- 101 -

Figure 8.3 (a) Synthetic Image, (b) Hough parameter space via projecting circles with

variable radius. High amplitude values (candidate center points) correspond to white pixels,

(c) Accumulator array, (d) Segmented image.

8.3 Results

To evaluate the performance of the proposed segmentation method, a comparative study was

employed, comprised 40 US thyroid images from 40 female patients between 40 and 65 years

old. All images were randomly chosen from a greater US image database collection acquired

from an experienced radiologist (N.D). The proposed method’s segmentation results were

compared with the delineated boundaries (used as ground truth) drawn from two experienced

observers (OB1 & OB2) in terms of nodule area, roundness, concavity and Mean Absolute

Distance (MAD).

The area of each nodule is calculated by measuring the pixels inside the nodule’s borders.

Roundness characterizes the circularity of the nodule and takes low values for circular nodule

and high for irregular boundaries [75]. The nodule’s roundness is defined as:

AreaPerimeterRoundness

2

= 8.10

The perimeter is measured by summing the number of pixels on the border of the nodule.

Concavity is a shape feature that indicates the presence of concave regions [75]. It is

measured by dividing the mean value of the Euclidean distances between the centroid and the


- 102 -

Convex Hull (CV) pixels with the mean value of the Euclidean distances between the centroid

and the Actual Boundary (AB) pixels:

∑

∑

=

=

−+−

−+−= M

iABCentroidABCentroid

N

iCVCentroidCVCentroid

ii

ii

XXYYM

XXYYNConcavity

1

22

1

22

)()(1

)()(1

8.11

The MAD characterizes the shape difference evaluation between two contours [162]. If two

given curves are represented as point sets: naaaA ,...,, 21= and mbbbB ,...,, 21= the

MAD describes the average pixel distance between these two curves:

⎭⎬⎫

⎩⎨⎧ += ∑∑ ==

m

i in

i i Abdm

Badn

BAe11

),(1),(121),( 8.12

with:

ijji abBad −= min),( 8.13

Regarding the MAD parameter, in order for the results to be numerically comparable with the

other three parameters the percentage MAD% parameter is introduced. It is considered as the

percentage pixel area difference between the automatic and manual boundaries. The distances

summation of each pair automatic (AU) – manual boundary (OB) is subtracted from the total

number of pixels within each manual boundary (OB). The result of this operation is converted

in terms of percentage. High MAD% values suggest that the great majority of pixels within the

manual boundary area (used as ground truth) are also present in the automatic boundary area

(see Equation 8.14).

%% ),( ⎟

⎠⎞⎜

⎝⎛ −= ∑ pixels

pixels AUOBdOBMAD 8.14

The comparison of the manually (OB1 & OB2) and the automatically (AU) segmented nodules

regarding area, roundness, concavity and MAD% gave agreement rates on average 88.95%,

91.77%, 91.09% and 90,64% respectively for the first observer and 87.58%, 91.12%, 89.08%

and 89,53% for the second observer.

The actual MAD values, calculated as the average of the distances, were 2.54 for the set of

pairs AU – OB1 and 2.16 for the set of pairs AU – OB2 with standard deviations 0.88 and 0.83

respectively. Results are presented in Tables 8.1 & 8.2.

Chapter 8

- 103 -

Table 8.1 Percentage agreement between automatic (AU) and manual segmentations (OB1,

OB2) in terms of Area, Roundness, Concavity and MAD%.

US Image

Area Roundness Concavity MAD% Average Accuracy

A/A AU- OB1

AU- OB2

AU- OB1

AU- OB2

AU - OB1

AU- OB2

AU - OB1

AU- OB2

AU- OB1

AU- OB2

1 84,55 90,65 91,63 94,44 90,19 92,53 90,70 90,19 89,27 91,95 2 85,31 78,94 92,78 97,08 93,11 96,33 93,44 93,11 91,16 91,37 3 84,82 90,40 92,79 92,03 86,61 86,71 85,93 86,61 87,54 88,94 4 86,92 91,21 91,97 94,68 90,91 95,19 93,72 90,91 90,88 93,00 5 87,99 85,71 93,65 90,36 95,87 81,94 92,01 95,87 92,38 88,47 6 86,13 82,49 90,93 94,22 94,94 87,61 87,87 94,94 89,97 89,81 7 95,00 88,96 89,42 89,51 83,80 89,62 86,81 83,80 88,76 87,97 8 87,22 94,22 93,78 84,48 84,24 85,49 87,47 84,24 88,18 87,11 9 94,52 88,51 90,29 95,51 89,19 92,12 89,23 85,12 90,81 90,31

10 82,89 82,64 93,03 96,77 88,75 92,90 93,55 88,75 89,56 90,27 11 87,40 80,97 91,88 93,12 82,64 90,54 91,94 82,64 88,47 86,82 12 94,20 91,15 93,64 86,59 80,63 88,93 94,94 88,12 90,85 88,70 13 87,27 84,31 86,90 88,07 83,65 89,72 90,10 83,65 86,98 86,44 14 90,68 84,19 96,73 93,53 87,44 81,52 89,98 87,44 91,21 86,67 15 85,90 78,96 93,27 89,12 97,86 90,32 92,05 97,86 92,27 89,07 16 82,30 91,24 93,93 90,23 98,01 95,20 85,21 93,19 89,86 92,47 17 88,86 95,09 75,51 81,76 89,26 84,14 88,62 89,26 85,56 87,56 18 88,81 91,25 95,27 93,43 91,66 87,57 93,16 91,66 92,22 90,98 19 93,80 88,08 92,48 93,27 85,31 85,58 87,08 85,31 89,67 88,06 20 87,30 86,83 94,09 95,67 93,16 95,32 95,71 93,16 92,57 92,75 21 91,04 94,50 93,45 95,48 89,18 85,49 92,09 89,18 91,44 91,16 22 90,86 87,05 89,19 85,80 76,27 82,45 90,01 84,11 86,58 84,85 23 84,95 76,00 94,10 89,86 92,20 84,10 89,33 92,20 90,14 85,54 24 88,37 84,23 96,21 93,48 92,01 86,11 85,12 92,01 90,42 88,96 25 88,16 86,08 96,70 92,31 92,98 88,93 92,53 92,98 92,59 90,07 26 93,82 97,93 95,00 91,21 95,12 96,24 91,53 95,12 93,87 95,12 27 94,64 90,71 93,37 87,35 81,38 90,76 91,14 81,38 90,13 87,55 28 92,84 88,71 94,39 96,12 88,93 93,70 93,37 88,93 92,38 91,87 29 93,44 95,12 90,43 92,31 87,72 83,43 90,13 87,72 90,43 89,65 30 96,86 91,13 87,07 89,95 93,30 85,21 87,99 93,30 91,30 89,90 31 95,26 94,02 95,59 96,78 86,59 90,03 96,96 90,12 93,60 92,74 32 81,52 81,61 87,19 91,78 90,96 89,51 93,38 90,96 88,26 88,47 33 93,49 89,03 95,02 84,46 96,07 92,27 92,52 96,07 94,27 90,46 34 77,87 78,68 88,81 84,56 82,93 91,36 92,19 83,98 85,45 84,65 35 84,91 84,08 91,92 89,34 82,60 88,44 93,53 84,56 88,24 86,61 36 80,55 79,31 93,94 92,68 93,14 91,24 94,44 93,14 90,52 89,09 37 83,19 84,63 92,44 94,55 93,63 86,12 91,96 93,63 90,31 89,73 38 92,47 96,88 92,91 93,51 89,97 96,71 84,65 89,97 90,00 94,27 39 94,83 91,16 79,91 84,12 86,60 84,97 91,73 86,60 88,27 86,71 40 92,30 86,59 89,16 85,19 89,46 86,91 86,53 89,46 89,36 87,04

Average accuracy 88,83

87,58

91,77 91,12 89,21 89,08 90,77 89,53 90,14 89,33

Table 8.2 Mean values and standard deviation of the computed MADs for the pairs AU –

OB1 and AU – OB2.

MAD (pixels) Standard Deviation

Automatic – Observer 1 (AU – OB1) 2.54 0.88

Automatic – Observer 2 (AU – OB2) 2.16 0.83

The overall segmentation procedure (edge detection – multiscale structure representation –

nodule’s boundary extraction) employed towards an efficient boundary detection in two US


- 104 -

images with an iso-echoic and a hypo-echoic thyroid nodule, is depicted in Figures 8.4 & 8.5

respectively.

Figure 8.4 (a) US image with an iso-echoic thyroid nodule, (b) Contour representation, (c)

Constrained Hough transform, (d) Accumulator array, (e) Outcome of the hybrid model, (f)

Manually delineated boundary.

Chapter 8

- 105 -

Figure 8.5 (a) US image with a hypo-echoic thyroid nodule, (b) Contour representation, (c)

Constrained Hough transform, (d) Accumulator array, (e) Outcome of the hybrid model, (f)

Manually delineated boundary.


- 106 -

Inter-observer variability: US regular diagnostic procedure is highly subjective, thus ideal

boundaries for the thyroid nodules are difficult to acquire. In order to assess any potential

variation in boundary recognition, an inter-observer study was also performed for the two

expert radiologists specialized in ultrasonography. The manual delineation in this study for all

US images was done independently. Inter - observer agreement was determined using the

weighted K (kappa) coefficient [117] calculated for all parameters employed in the previous

comparative study. The ideal boundary was selected as the vector space union of each manual

borderline pair. The threshold chosen for each parameter, in order for a manual boundary to

coincide with the ideal one, was set to 90% agreement. A kappa statistic above 0.75 is taken

arbitrarily to show excellent agreement, between 0.40 and 0.75 as substantial agreement and

below 0.40 as poor agreement – Table 8.3.

Table 8.3 Inter-observer agreement (kappa coefficient) between the two observers

Kappa Coefficient

Area 0.89

Roundness 0.77

Concavity 0.75

MAD 0.92

Average 0.83

The comparison of the two manually segmented nodules regarding area, roundness, concavity

and MAD gave agreement rates on average approximately 90.77%, 91.39%, 92.25% and

92.91% respectively with an overall percentage agreement of 91.83%.

8.4 Discussion and Conclusion

A new segmentation technique for automatic boundary extraction of thyroid nodules in US

imaging is designed. The contribution of this approach is the integration of wavelet-based

coarse to fine singularity detection, multiscale structure model, and the constrained Hough

transform. In the comparative study, thyroid nodule segmentation accuracy reached

approximately 90.14% and 89.33% in respect with the two observers. The percentage

agreements between the derived and the manual delineated boundaries are within the inter-

observer range (91.83%). The MAD values, between the derived and the manual delineated

boundaries (2.16 – 2.54), also coincide with the values other studies have presented (1.37 to

4.55) [122,135,136]. The inter-observer study demonstrated high kappa coefficient agreement

of approximately 0.83. Although the algorithm is unsupervised, the evaluation results may be

regarded as most encouraging considering the reduced US image quality. The proposed

Chapter 8

- 107 -

algorithm may be of value for computer-assisted systems aiming to support the standard

diagnostic procedure as an objective second opinion tool.

The local maxima representation employed to construct the speckle free – multiscale edge

map not only does it identify edges but also characterizes them. The integration of local

maxima via a coarse to fine method led to the different classification of edges based on their

regularity. As a result, strong edges arising from significant structures are utilized in the

subsequent structure model, whereas edges corresponding to speckle were discarded.

Regarding the maxima chaining procedure, similar maxima linking attempts [70,163] have

adopted a thresholding procedure based on the number of adjacent local maxima only in the

last scale available to isolate the ROI. The complex nature of US imaging often provides

maxima chains with relatively small number of linked local maxima (two or three contiguous

maxima) that might be a part of a greater structure contour. In contrast to these studies, the

proposed multiscale structure model utilizes all local maxima existing in the edge map across

scales, in order to reconstruct the best possible contour map.

Besides the presence of speckle, another major difficulty that all segmentation approaches

encounter, is the existence of various anatomical structures located within the image. In very

noisy structural environments, ROI isolation is an extremely difficult task. Most proposed

methods also attempt to calculate a closed contour as a final segmentation outcome. The

constrained Hough transform employed in this study, not only is it relatively unaffected by

structure noise, but manages to isolate all thyroid nodules despite the fact that sometimes the

nodule contour is not closed. In cases of diffusion between the nodule and the surrounding

tissue, the algorithm does not guess the nodule boundary in that region, thus leaves this

important clinical information for the physician. In addition, due to the fact that nodules are

not perfect circles, the radius of the contour is variable and the accumulator array local

maxima detection is made in a small area rather than in a single point.

The different echogenicity behavior of thyroid nodules (hypo-, iso- or hyper-echoic) limits the

accuracy of thyroid nodules segmentation algorithms based on texture characteristics [164].

The edge-based technique presented in this article is echogenicity invariant as we can observe

in Figures 8.4 & 8.5, in which an iso-echoic and a hypo-echoic nodule are successfully

segmented. Apparently, the hybrid algorithm can be employed to segment various anatomical

structures viewed via US imaging with only one constrain: The ‘a-priori’ shape knowledge

selection regarding the structure of interest.

The outcome of the edge detection stage is highly depended on the radiologist’s competency

in performing the US examination. Any possible misplacement of the transducer or the

occurrence of various acoustic phenomena such as reverberation or shadowing, may produce

a false contour map. The proposed algorithm identifies sharp variations with great accuracy

wherever they occur but don’t approximate the edges that are not visible in the image. In US


- 108 -

images, where the thyroid nodule is partially visible or greatly distorted due to

aforementioned acoustic phenomena, the proposed algorithm faced problems during the edge

detection procedure. All the cases that had these drawbacks were omitted from the

comparative study.

The incorporation of the generalized form of the Hough transform for arbitrary shape

detection into the maxima chaining procedure across scales, may avoid most of the problems

encountered by the majority of edge detection approaches. Nevertheless, the fine-tuning

between the inter-scale wavelet maxima chaining and Hough transform algorithms, along

with the extensive compilation time of the Hough transform are main drawbacks towards this

segmentation approach. The aforesaid potential problems of any segmentation approach

necessitate the continuous investigation for an optimal segmentation technique. A parallel

wavelet-based study is under research and development from the same team, based on zero

crossings detection in which the wavelet transform is made with the second derivative of a

Gaussian smoothing function.

As a conclusion, a new efficient segmentation technique for thyroid nodule segmentation in

sonography is introduced with promising results. The proposed algorithm is able to outline

with high accuracy thyroid nodules regardless their texture, possible discontinuities in the

boundary line and the presence of extensive structure noise. The method was evaluated in

comparison with two experienced observers and demonstrated great agreement accuracy. The

utilization of the hybrid method may assist a shape-based thyroid nodule categorization from

the physician. Also, it might enhance the accuracy of the fine needle aspiration procedure thus

offer several advantages in the decision-making procedure. Moreover it can be used as an

educational tool for inexperienced radiologists.

- 109 -

CHAPTER 9

Development of a Support Vector Machine – Based Image

Analysis System for Assessing the Thyroid Nodule Malignancy

Risk on Ultrasound

Summary

In this chapter an image analysis system, based on the support vector machine (SVM) classifier is

introduced for the automatic characterization of thyroid nodules in sonographic images that

employed textural features. The chapter is organised as follows: at first a review of the literature

regarding clinical and computer based attempts to categorize thyroid nodules is presented. In the

materials and methods sections the SVM classifier is presented along with the classical quadratic

least squares minimum distance (QLSMD) the quadratic Bayesian (QB) and the multilayer

perceptron (MLP) classifiers for comparison reasons. In the results section the performance of the

SVM classifier compared to that of the other three classifiers is also presented. Moreover a study

regarding the design and implementation of wavelet kernels built within the framework of

Reproducing Kernel Hilbert Spaces (RKHS) is introduced. In the discussion section a detailed

analysis regarding performance and clinical aspects raised from the algorithm’s results is given.


Thyroid nodules are swells that appear in the thyroid gland and can be due to growth of thyroid

cells or a collection of fluid known as cyst. They can become large enough to press on nearby

structures in the neck, they can overproduce thyroid hormone (hyperthyroidism) or they may be

indicative of thyroid cancer [1]. Various techniques have been introduced for the detection and

evaluation of thyroid nodules such as physical examination, cytological examination,

scintigraphy, ultrasonography, magnetic resonance, and computed tomography [14].

High-resolution thyroid ultrasonography (US) is exceptionally sensitive in locating the size and

number of thyroid nodules [19]. The sonographic findings of the thyroid nodule are often

employed as criteria in assessing the risk factor of malignancy and are crucial in patient

management, i.e. whether to recommend or not surgical operation [19]. Such criteria include

echogenicity, absence of halo, calcifications, irregular margins, and intra-nodular vascular

patterns or spots [20,22]. However, estimation of the risk factor involves the subjective evaluation

Development of an SVM Model for Assessing Thyroid Nodule Malignancy Risk

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of US images by the physician and, thus, it depends upon the experience of the examiner.

Previous US studies [5,17,18,21,25,27] on thyroid nodules have reported different diagnostic

accuracies in predicting malignancy based on the visual analysis of US images. It is evident that a

quantitative assessment of the thyroid nodule’s risk factor may be of value in avoiding

unnecessary invasive interventions.

Previous studies on quantitative methods for estimating the risk associated with thyroid gland

disease mainly concern evaluation of parameters from the gray-level histogram of the thyroid

gland US image [165,166], several textural features from gray-tone spatial-dependence matrices

[167] and the application of discriminant analysis [165,167]. In those studies, discrimination

accuracies between benign and malignant thyroid nodular lesions were 83.9% [167] and 85%

[165]. The fact that echogenicity and the existence of different structures inside the thyroid

nodule have been indicated as important factors leading to thyroid malignancy [17,18,25,27],

combined with the lack of recent quantitative studies in assessing the nature of thyroid nodules,

necessitates research to continue employing: (a) US thyroid images of modern high resolution

scanners and (b) robust computer-based pattern recognition methods using state-of-the-art

classification algorithms to increase the classification accuracy of objective methods and thus

assist physicians in the pre-operative management of patients.


9.2.1 US Image Data Acquisition

The study comprised 120 ultrasonic images displaying thyroid nodules of 120 patients. All US

examinations were performed on an HDI-3000 ATL digital ultrasound system – Philips

Ultrasound P.O. Box 3003 Bothel, WA 98041-3003, USA – with a wide band (5-12 MHz) linear

probe using various scanning methods such as longitudinal, transversal and sagittal cross sections

of the thyroid gland. The dataset was acquired in the time interval from October 2003 to

September 2004. During ultrasound examinations the ‘SmallPartTest’ Philips protocol was used.

All protocol’s settings remained constant throughout that period. Time gain compensation-setting

had a linear increasing gain compared to the depth. Magnification setting remain 1:1 except rare

cases of very small nodules (<1.5 cm), which were not included in the present study. Dynamic

range setting was relatively high (60 dB) in order to exploit the high capability of contemporary

US systems to visualise US images with the maximum number of gray tones. Thermical and

mechanical indexes were set at 0.2 and 0.9 respectively. Multiple focal lengths were set at 1, 2

and 3 cm simultaneously.

Chapter 9

- 111 -

Each US image was digitized via connecting the video output of the ultrasound scanner to a

Screen Machine II frame grabber using 768 x 576 x 8 image resolution. Under real-time

ultrasound guidance, all nodules with size above 1.5 cm underwent fine needle (23-gauge)

aspiration biopsy. From various sites of the nodules 6 to 10 specimens were taken and smears

were placed in slides. Those slides were evaluated from two experienced observers. Excluding the

rare cases of typical neoplasm of the thyroid both observers graded the cases in two major

categories: epithelial hyperplasia which can be characterised as high risk (42 cases) due to

potential malignancy growth, thus leading to repeated ultrasound and cytology examinations of

the patient, and in benign lesions (colloid nodules – 78 cases), in which the follow up

examinations can be performed in long time intervals. Retrospectively the physician (N.D)

analysed the US characteristics of the corresponding ultrasound images of the two classes given

by the cytologists in accordance with Tomimori’s grading [20]. The low risk class mostly

comprised iso-echoic or hyper-echoic solid nodules with or without cystic change and coarse

calcification while the majority of the high-risk class contained hypo-echoic solid nodules with

regular borders or cystic nodules with solid components.

9.2.2 Data Pre-processing

The boundary of each nodule was delineated by the physician employing an easy-to-use

interactive software program implemented for the purposes of the present study. Data processing

was performed on an AMD Athlon XP+ processor running at 1.8 GHz and 512 of RAM. A

number of textural features were automatically calculated from the segmented ROI of each

thyroid nodule. Textural features are related to the gray-tone structure of the thyroid nodule as

depicted on the ultrasound unit and carry information relevant to the risk factor of malignancy.

Four features were computed from the nodule’s gray-tone histogram, 26 from the co-occurrence

matrix [73] and 10 from the run-length matrix [74].

9.2.3 Classification

System evaluation was performed by means of the leave-one-out methods (LOO) [83] and highest

classification accuracies were determined by means of the exhaustive search method [83].

Besides LOO method, the re-substitution method was also employed (all data were involved in

the design and evaluation of the classifier), so as to find the upper and lower bounds of the

classification error [83]. For the purposes of the present study four classifiers were designed, the

Support Vector Machine classifier and for comparison reasons the QLSMD, the QB and the MLP

classifiers. In the design of a classifier, features play an important role that influences its final

discriminatory performance. Ideally, all features at hand (40) should be employed, but since a


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number of them may be redundant due to mutual correlations [83], an optimum number of them

had to be selected to achieve highest classification accuracy. Choosing the best feature

combination that will maximize the performance of the classifier is a necessary but time-

consuming and computationally demanding procedure. The method followed (exhaustive search)

involved designing the classifier by means of every possible feature-combination (i.e. 2, 3, 4

feature combinations) and all thyroid data available, each time testing the classifier’s performance

in correctly classifying the thyroid data, and finally selecting that feature combination that

demonstrated the highest classification accuracy with the smallest number of textural features.

The exhaustive search method was chosen instead of statistical methods such as F-statistics,

because the latter could result in unreliable error probability estimation [83], due to small size of

the dataset.

For the SVM-classifier [87, 88, 168] employing the polynomial kernel of 3rd degree, best feature

combination comprised the mean gray-level (Chapter 6 – Equation 6.1) value of the thyroid

ROI’s histogram and the sum variance (Chapter 6 – Equation 6.16) from the co-occurrence matrix

[73].

For the MLP classifier the highest classification accuracy was achieved by the mean gray-level

value (Chapter 6 – Equation 6.1) and the run length non-uniformity (Chapter 6 – Equation 6.26)

from the run length matrix [74].

For both the QLSMD and QB classifiers, highest classification accuracies were achieved by the

feature combination of the mean gray-level value, the sum variance, and the run length non-

uniformity.

9.2.4 Support Vector Machine Classifier

An SVM based classifier is designed to work for two class-problems and it can be applied to

linearly or non-linearly separable data, with or without class data overlap [87]. In the most

difficult case of non-linearly separable and overlapped data, which is often the case, data are first

transformed from the input space to a higher dimensionality feature space, where classes are

linearly separable. Then two parallel hyperplanes are determined with maximum distance

between them and at the same time with minimum number of training points in the area between

them (also called the margin). Finally, a third hyperplane through the middle of the margin is

defined, which is the decision boundary of the two classes. The discriminant equation of the SVM

classifier may thus be defined as in (9.1):

Chapter 9

- 113 -

⎟⎟⎠

⎞⎜⎜⎝

⎛+= ∑

=bkysignxg

SN

iiii

1),()( xxα 9.1

where ai are weight parameters, k(xi,x) is the kernel function employed for the data

transformation into the linearly-separable feature space, xi are the support vectors (i.e. the training

pattern vectors that have their corresponding weights ai ≠ 0), NS is the number of support vectors,

x is the input pattern vector, b is the bias or threshold, and yi ∈ –1, +1, depending on the class.

In the present work, the SVM classifier was designed employing various polynomial kernels up to

the 4th degree (Chapter 6 – Equation 6.61) and the radial basis function (Chapter 6 – Equation

6.62) kernel.

9.2.5 Multilayer Perceptron (MLP) Classifier

The MLP classifier employed in this study is a feed-forward back propagation neural network

that has two input features, two classes, two hidden layers and four nodes in each hidden layer

(for more details see Chapter 6, paragraph 6.6.3).

9.2.6 Quadratic Least Squares Minimum Distance Classifier

The QLSMD classifier [169] maps via a non-linear transformation the input data set into a

decision space where each class is clustered around a pre-selected point. The classification of a

given test point is based on its minimum distance from each pre-selected point. For the QLSMD,

the discriminant function for class i and for pattern vector x is given by:

bxxxxg j

d

jijkj

d

j

d

ikiji

d

jiji −++= ∑∑ ∑∑

=

−

= +== 1

1

1 1

2

1

)( αααx 9.2

where d is the number of features, αij are weight elements, b is a threshold parameter, and xj are

the input vector feature elements.

9.2.7 Quadratic Bayesian Classifier

The Bayes decision theory develops a probabilistic approach to pattern recognition, based on the

statistical nature of the generated features. The Bayes discriminant function [170] for class i and

for pattern vector x is given by:

gi(x) = lnPi – 21 ln|Ci| – 2

1 [(x – mi)TCi-1(x – mi)] 9.3

where Pi is the probability of occurrence of class i, mi is the mean feature vector of class i, and Ci

is the covariance matrix of class i.


- 114 -

9.2.8 Support Vector Machines Wavelet Kernels

In this section the efficiency evaluation of wavelet kernels within the SVM classifier model for

the characterization of the malignancy risk factor of thyroid nodules in sonographic images is

introduced. The SVM classifier designed in this study was based in wavelet kernels built within

the framework of Reproducing Kernel Hilbert Spaces (RKHS) [171,172]. Several periodized

orthogonal wavelets were used (Daubechies, Coiflett, Symmlet,) for the construction of the

corresponding reproducing kernels and their performance was compared to that of the standard

polynomial and radial basis function kernel functions.

9.2.8.1 Wavelet Kernels Implementation

A reproducing kernel Hilbert space is a Hilbert space of functions with special properties [173]

and along with its associated kernels can be constructed by means of the frame theory

[174,56,175]. Frame theory analyzes the completeness, stability and redundancy of linear discrete

signal representations. A frame is a family of vectors ΓΦ nn that characterizes any signal f

from its inner products ΓΦ nf n, . Frame theory allows the representation of any vector in

space by linear combination of the frame elements. The discrete wavelet transform is studied and

developed through the frame formalism.

Building RKHS from a Hilbert Space: Below are presented the conditions under which a

frameable Hilbert Space is also a Reproducing kernel Hilbert Space. Let B be a functional Hilbert

Space Η endowed with inner product B

⋅⋅, so that:

∞<∈∀B

fBf , 9.4

In order to build an RKHS from that Hilbert space, an operator T is defined to map the H

functions onto the set of the pointwise valued functions : RXfR X →= . A general way of

constructing such a linear mapping is based on the scalar product. We define a set of functions

Β∈⋅Γ )(x [176], indexed by Xx∈ and the mapping operator T:

XRB →

T: )(⋅→ gf so that

Bx fxTfxg )(,)()()( ⋅⋅Γ==Δ

9.5

B is decomposed to MTKerB ⊕= )( and the bijective restriction of T is called S

Chapter 9

- 115 -

)Im(THM =→

S: TSfgf ==⋅→ )(

9.6

If H is endowed with the following inner product

BBggHffSSggHgg 21

112121 ,,,,,

21==∈∀ −−

Δ 9.7

Then H is a RKHS [173] with a Reproducing Kernel K in H:

HyxyxK ),(,),(),( ⋅Γ⋅Γ= 9.8

According to Aronjain theorem [173] for any RKHS space of functions exist a reproducing kernel

and vice versa. This reproducing kernel constitutes a Mercer Kernel [177].

Construction of wavelet kernel in )(2 XL : The dilated and translated wavelet family φi

constitutes an orthonormal basis of L2 (R) space in which underlie a wavelet functions Hilbert

space [171, 172].

We restrict to cases where B=L2 and 2LH ⊂ . Consider the wavelet family φi as an

orthonormal basis of L2. Since )(⋅Γx is a function set of L2 and 2LH ⊂ , we denote:

∑ ⋅=⋅Γ∈∀ji

ijjix xaXx,

, )()()(, φφ 9.9

with, ∑ ∞<i

i xa )(2 9.10

where )(⋅ia being a set of coefficients depending on the evaluation point x. This equation

supposes that )(xiφ exist and is well defined for Xx∈ . In other words, this means that the

considered orthonormal basis must be defined pointwise. The reproducing kernel of H becomes:

∑=⋅Γ⋅Γ=nji

njnijiyx yxaayxK,,

,, )()()(,)(),( φφ 9.11

For each classification problem in SVMs, a hypothesis space associated with a kernel K built

from an operator )(⋅Γx is expressed as:


- 116 -

∑=⋅Γ⋅Γ=kj

kjkjkjyx yxayxK,

,,2, )()()(,)(),( ψψ 9.12

where kj ,ψ is a translated 1-dimensional wavelet of resolution j: [171, 172].

⎟⎟⎠

⎞⎜⎜⎝

⎛ −= j

j

jkj aakux

ax 0

,1)( ψψ 9.13

9.2.9 System Performance Evaluation

System evaluation was performed by means of the leave-one-out method. Accordingly, each

classifier was designed employing its best feature combination determined in section 2.3 and by

all but one thyroid-ROI feature vector. The latter was presented to the input of the system to be

classified as either high-risk or low-risk. The process was repeated, each time leaving a different

thyroid-ROI out, until all data had been processed. In this way, each classifier was evaluated by

data that were not involved in its design. It is evident, that the classifiers had to be re-designed

each time a thyroid-ROI was left out. This required few hours of computer processing time.

9.3 Results and Discussion

We have developed a quantitative method by means of an SVM based software classification

system that employed a large number of textural features from US thyroid images for assessing

the malignancy risk factor of thyroid nodules.

9.3.1 SVM Classification Outcome

Table 9.1 shows the results obtained by the SVM classifier for different kernel functions. Results

were obtained by the leave-one-out method and by the re-substitution method. Maximum

classification accuracy in distinguishing low-risk from high-risk thyroid nodules by the LOO

method was 96.7% using the polynomial kernel of 3rd degree.

Table 9.1 Classification accuracies for various SVM kernels using the leave-one-out and re-

substitution methods, for the “mean gray value – sum variance” best feature combination

Classification accuracy SVM kernel LOO+ (%) Resub.* (%) NSV**

Polynomial of 1st degree 89.2 93.3 17 Polynomial of 2nd degree 91.7 96.7 13 Polynomial of 3rd degree 96.7 98.3 12 Polynomial of 4th degree 94.2 99.2 15 RBF 94.2 97.5 15 + Leave-one-out method

Chapter 9

- 117 -

* Re-substitution method ** Number of support vectors employed using the re-substitution method

It’s worth noting that the maximum classification accuracy corresponds to the minimum number

of support vectors involved in the design of the SVM-classifier. The number of support vectors

among different kernel functions for the best feature combination ranged between 10% and 14.2

% of the number of training points. The small number of support vectors is indicative of the SVM

manageable class separability.

Table 9.2 gives a detailed account of the SVM-3rd degree polynomial kernel classification

accuracies obtained by the LOO and re-substitution methods, employing the mean gray-level

value and sum variance features combination.

Table 9.2 Truth table of the SVM classifier employing the 3rd degree polynomial kernel, and the

“mean gray value – sum variance” best feature combination

SVM classification (3rd degree polynomial kernel)

Verified thyroid nodule classes Low risk High risk LOO+ (resub.*)

accuracy Low risk 76 (78) 2 (0) 97.4 (100) % High risk 2 (2) 40 (40) 95.2 (95.2) %

Overall accuracy 96.7 (98.3) % + Leave-one-out method * Re-substitution method

Seventy-six of the low-risk thyroid nodules were correctly classified while two nodules were

incorrectly assigned to the high-risk class, giving a classification accuracy of 97.4% by the LOO

method. In the case of the high-risk thyroid nodules, forty were assigned to the correct class while

only two were wrongly classified to the low-risk class, scoring a 95.2% class discrimination

accuracy. Overall, the SVM achieved 96.7% precision in distinguishing correctly low-risk from

high-risk thyroid nodules.

Figure 9.1 shows a scatter diagram of the mean gray-level value against sum variance, the class

margins and the decision boundary drawn by the SVM-3rd degree polynomial kernel classifier.


- 118 -

Figure 9.1 “Sum variance” versus “mean gray value” scatter diagram, displaying the low-risk and

high-risk thyroid nodule data points, the SVM classifier margins, and the decision boundary

employing the polynomial kernel of 3rd degree.

The best features combination employed (mean gray-level value and sum variance) are related to

the textural parameters visually evaluated by physicians in assessing the thyroid nodule’s risk

factor [17, 18, 25, 27]. The mean gray-value is closely associated with the echogenicity of the

nodule and the sum variance feature expresses useful spatial information inside the nodule linked

to the existence of various structures within the nodule. Features of relative nature (upper 10%

gray-level histogram distribution and entropy) have also been indicated in previous quantitative

studies [164] to play an important role in thyroid nodule malignancy assessment, scoring an

overall of 85% classification accuracy. Similar accuracies (83.9%) were also obtained in another

quantitative study employing discriminant analysis of thyroid nodules [166]. The higher

discriminatory precision achieved in the present study was most probably due to the improved

resolution of the US-images and to the non-linear nature of the highly sophisticated SVM

algorithm employed.

Chapter 9

- 119 -

9.3.2 MLP Classification Outcome

Table 9.3 gives a detailed account of the MLP classification accuracies obtained by the LOO and

re-substitution methods, employing the mean gray-level value and Run Length Non Uniformity

features combination. Figure 9.2 shows a scatter diagram of the mean grey-level value against

Run Length Non Uniformity and the decision boundary drawn by the MLP classifier.

Table 9.3 Truth table of the MLP classifier employing the “mean gray value – Run Length Non

Uniformity” best feature combination.

MLP classification Verified thyroid nodule

classes Low risk High risk LOO+ (resub.*) accuracy

Low risk 73 (75) 5 (3) 93.6 (96.2) % High risk 1 (1) 41 (41) 97.6 (97.6) %


Figure 9.2 “mean gray valu\e”, and “run length non-uniformity” scatter diagram, displaying the

low-risk and high-risk thyroid nodule data points and the MLP classifier decision boundary.


- 120 -

Both features employed by the MLP classifier represent the echogenicity of the thyroid nodule

(mean grey value) and the possible existence of micro-calcifications or other structures (RLNU)

within the nodule’s environment.

9.3.3 QLSMD & QB Classification Outcome

Regarding the classical QLSMD and QB classifiers, their classification precision dropped when

they were employed as shown in Tables 9.4 and 9.5 respectively.

Table 9.4 Truth table of the QLSMD classifier employing the “mean gray value – sum variance –

run length non-uniformity” best feature combination

QLSMD classification Verified thyroid nodule classes Low risk High risk LOO+ (resub.*) accuracy



Table 9.5 Truth table of the QB classifier employing the “mean gray value – sum variance – run

length non-uniformity” best feature combination.

QB classification Verified thyroid nodule classes Low risk High risk LOO+ (resub.*) accuracy



Table 9.4 is the truth table giving the classification performance of the QLSMD classifier

using the best feature combination (mean gray-level value, sum variance, and run length non-

uniformity). Seventy-four of the low-risk and 37 of the high-risk thyroid nodules were correctly

classified using the LOO method, resulting in group classification accuracies of 94.9% and 88.1%

respectively and overall precision of 92.5%. Similarly, Table 9.5 presents the results obtained by

the QB classifier. Although the QB overall accuracy (92.5%) was similar to that obtained by the

QLSMD classifier, the corresponding group accuracies differed to 93.6% and 90.5% for the low-

risk and high-risk thyroid nodules respectively. These differences are insignificant and may be

attributed to differences in the nature of the algorithms. The third feature employed (run length

non-uniformity) by MPL, QB and QLSMD classifiers signifies the existence of structures of

Chapter 9

- 121 -

different sizes within the thyroid nodule, which is related to the optical criteria employed by

physicians in assessing the nodule’s risk factor for malignancy [17, 18, 25, 27].

Figures 9.3 and 9.4 show the 3-dimensional scatter diagrams of the mean gray-level value, sum

variance, and run length non-uniformity, as well the decision boundaries drawn by the QB and

QLSMD classifiers respectively.

Figure 9.3 “Sum variance”, “mean gray value”, and “run length non-uniformity” scatter diagram,

displaying the low-risk and high-risk thyroid nodule data points and the QB classifier decision

boundary.


- 122 -

Figure 9.4 “Sum variance”, “mean gray value”, and “run length non-uniformity” scatter diagram,

displaying the low-risk and high-risk thyroid nodule data points and the QLSMD classifier

decision boundary.

Comparing the SVM with these two classical classifiers it is evident that the latter had to employ

an extra feature to enhance their performance, however without reaching the SVM’s precision.

This is indicative of the effectiveness of the SVM. The penalty, however, that had to be paid for

employing the SVM algorithm was much higher processing time during classifier design

(training). We have tackled the above problem by suitably distributing computer processing to

different workstations and by using the re-substitution method to find well-behaved feature

combinations with high classification accuracies and small numbers of support vectors (i.e.

leading to separable classes) prior to system evaluation by the LOO method.

9.3.4 SVM with Wavelet Kernels Classification Outcome

The wavelet kernel construction procedure is a multi-parametric approach comprised of the

wavelet family selection, the number of vanishing moments for each wavelet and its

corresponding scaling function, in addition with the number of the dyadic decomposition. In order

to avoid the unconscionable processing time of the leave-one-out method for all possible

Chapter 9

- 123 -

combinations that would preclude any possible fine tuning of the above mentioned parameters,

the wavelet kernel evaluation was constricted to the best fifty features combinations obtained by

the SVM classifier with the 3rd degree polynomial kernel which in our study exhibited the highest

classification accuracy. The wavelets families employed in the present study were the periodized

orthogonal Daubechies, Coiflet and Symmlet. The aforementioned wavelets had their support in

the interval [2, 10] whereas the dyadic decomposition ranged from 20 to 29.

The fine tuning of the wavelet kernel parameters led to a significant number of different

combinations. Best feature combination for all wavelet kernels was similar to that of the 3rd

degree polynomial kernel (mean gray value & sum variance). Maximum classification accuracy

was achieved for the Daubechies, Coiflet and Symmlet wavelet kernels with 3,8 and 6 vanishing

moments and a 27, 27 and 29 decomposition scales respectively (Table 9.6). Tables 9.7, 9.8 and

9.9 give a detailed account of the SVM – wavelet kernels classification accuracies obtained by the

LOO and re-substitution methods, employing the mean gray-level value and sum variance

features combination.

Table 9.6 Classification accuracies for various SVM wavelet kernels using the leave-one-out and

re-substitution methods, for the “mean gray value – sum variance” best feature combination

Classification accuracy SVM kernel LOO+ (%) Resub.* (%) NSV**

Daubechies Wavelet Kernel 95.8 98.3 9 Coiflet Wavelet Kernel 97.5 100.0 10 Symmlet Wavelet Kernel 95.0 99.2 10 + Leave-one-out method * Re-substitution method ** Number of support vectors employed using the re-substitution method

Table 9.7 Truth table of the SVM classifier with the Daubechies wavelet kernel employing the

“mean gray value – sum variance best feature combination

SVM classification Verified thyroid nodule classes Low risk High risk LOO+ (resub.*) accuracy



Table 9.8 Truth table of the SVM classifier with the Coiflet wavelet kernel employing the “mean

gray value – sum variance best feature combination



- 124 -



Table 9.9 Truth table of the SVM classifier with the Symmlet wavelet kernel employing the

“mean gray value – sum variance best feature combination




Figures 9.5, 9.6, 9.7 shows a scatter diagram of the mean gray-level value against sum variance,

the class margins and the decision boundary drawn by the SVM classifier employing the

Daubechies, Coiflet and Symmlet wavelet kernels respectively.


Chapter 9

- 125 -

High-risk thyroid nodule data points, the SVM classifier margins, and the decision boundary

employing the Daubechies wavelet kernel.


high risk thyroid nodule data points, the SVM classifier margins, and the decision boundary

employing the Coiflet wavelet kernel.


- 126 -


high-risk thyroid nodule data points, the SVM classifier margins, and the decision boundary

employing the Symmlet wavelet kernel.

Wavelet kernels achieved analogous performance compared to standard kernels with substantially

lesser number of support vectors (The number of support vectors among different wavelet kernel

functions for the best feature combination ranged between 7.5% and 8.3 % of the number of

training points.) thus improving their generalization ability. The processing time is even higher

than that of the classical kernels due to wavelet construction procedure. Reproducing kernel

Hilbert spaces framework is widely used in regularization theory, regression and function

approximation [178–184]. The fact that for every Hilbert space of functions exists a reproducing

kernel function suggests some of the power and insight that the RKHS affords. The classification

power of SVMs comes directly from the complexity of the underlying kernel. The wavelet

kernels parameterization can be interpreted as flexibility against a particular dataset. Both Mercer

condition and frameable RKHS allowed obtaining a definite positive function. However, it is

obvious that conditions for having frameable RKHS is easier to verify than Mercer condition.

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CHAPTER 10

Pattern Recognition Methods Employing Morphological and

Wavelet Local Maxima Features towards Evaluation of

Thyroid Nodules Malignancy Risk in Ultrasonography

Summary

In this chapter, a new approach is presented towards thyroid nodules automatic classification in

terms of potential malignancy growth. It employs morphological and wavelet-based features

derived from each nodule’s ROI that was automatically extracted via a multi-scale hybrid model

[195]. The chapter is organized as follows: In the material and methods section an extensive

analysis is given, of the patients set and the feature extraction procedure derived from each ROI’s

local maxima edge map. In the results and discussion a parallel study is held with two well known

pattern recognition algorithms (SVMs and PNNs). The design and implementation of both

classifiers involved the local maxima directly derived from the multiscale edge representation

[62] and those obtained from inter-scale regularity estimation for speckle suppression [196]. In all

cases a thorough discussion is presented regarding the clinical importance of the morphological

and wavelet-based features.


10.1.1 Patients

The study comprised 85 patients; each one of them has undergone high-resolution US

examination of the thyroid gland with an HDI-3000 ATL ultrasound system (Philips Ultrasound,

Bothel, WA, USA) equipped with a wide band 5 – 12 MHz linear transducer. The data set was

acquired in the time interval from February 2005 to August 2006 in the Medical Imaging

Department – Medical Center EUROMEDICA, Athens, Greece. All US examinations were

performed with the ‘SmallPartTest’ built-in protocol from Philips. The system’s settings (Time

Gain Compensation TGC, magnification, dynamic range, focal lengths etc) remained constant

throughout the study period [194]. Each US image was digitized (768 x 576 x 8 bit) using a

Screen Machine II frame grabber directly connected to the video output of the US system. In each

Morphological and wavelet features towards thyroid nodule malignancy evaluation

- 128 -

patient with thyroid nodules sized above 1.0 cm, real time sonographically guided FNA (23-

gauge) biopsy was performed. Five or more passes were made through the nodule and smears

were withdrawn by capillary action and placed in slides. Of the 85 cases evaluated by two

observers, 54 were diagnosed as benign lesions (Low Risk – 54 cases) and 31 as lesions with

epithelial hyperplasia (High Risk – 31 cases). Low risk thyroid patients with possible colloid

nodules require long time intervals between consecutive examinations, whereas in high risk

patients frequent US and cytology examinations are necessary (Figure 10.1).

Figure 10.1 US images representing various morphologic types of Low-Risk and High-Risk

Thyroid nodules.

From each US image, a set of morphological and wavelet local maxima features was extracted to

encode the malignancy risk factor of thyroid nodules and classification was performed using the

SVM and PNN classifiers.

10.1.2 Feature Extraction

The boundary of each thyroid nodule was extracted through a hybrid multi-scale model that

integrated in a cascade level at first a speckle reduction – edge detection procedure that employed

dyadic wavelet transform and local maxima regularity estimation. Consequently, a multi-scale

structure model for boundary detection, and finally the Hough transform for the boundary nodule

extraction [195]. The regularity detection has been employed in maxima chains that consist of

local maxima that back-propagate towards the finer available scale. These maxima possess

similar position and angle values in the inter-scale level. In maxima chains where the amplitude

of the wavelet transform modulus maxima decreases along with the scale the Lipschitz regularity

is positive. When the maxima amplitude increases while the scale decreases the Lipschitz

Chapter 10

- 129 -

regularity is negative. The maxima with positive Lipschitz exponents were considered as edges

that correspond to important image features, whereas the maxima with negative Lipschitz

exponents were classified as speckle [196]. The edge map utilized in the local maxima feature

extraction was derived both prior and after the regularity estimation so as to evaluate the speckle

effect in the classification accuracy.

A set of 20 morphological and local maxima features was extracted (Table 10.1) from the

segmented nodules describing each individual case – patient. Morphological features describe the

shape and size of each nodule (12 features) and comprised area, roundness concavity, fractal

dimension etc [185,190,75]. Local maxima features derived from speckle and speckle-free edge

map, encode information regarding the presence of micro-calcifications (MCs) and the variability

of the echogenicity inside the nodule’s boundary (8 features). The classification procedure was

performed independently in the speckle and speckle-free feature sets for both classifiers.

Table 10.1 Morphological and Local Maxima Features of Thyroid Nodules

Morphological Features Local Maxima (LM) Features

a/a a/a 1 Radius 1 First Order Histogram 2 Radius Entropy 2 Mean Value 3 Radius Standard Deviation 3 Entropy 4 Perimeter 4 Central Moment(3rd Degree) 5 Area 5 Kurtosis 6 Circularity 6 Skewness 7 Smoothness 7 Variance 8 Convex Hull Radius 8 Standard Deviation 9 Concavity

10 Number of Concave Points 11 Symmetry 12 Fractal Dimension

10.1.3 Feature Selection and Classification

The optimum goal in the design of a classifier with a given feature set, is the selection of the most

important features with the minimum number of them without the loss of their discriminatory

information. The feature selection procedure employed in the present study towards highest

likelihood of prediction, was made by exhaustively combining all pre-selected features in any

possible combination (2, 3, 4, feature combinations). The training of the classifiers is performed

by means of the leave-one-out (LOO) method. In LOO method the training is performed in all but

one feature vector. The depiction of each best features combination scatter diagram and the

decision boundary for both classifiers is made with the Re-substitution (Re-Sub) method. Re-Sub

method utilized the same feature vector at first for training and then for testing [83]. System


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evaluation was performed by means of Receiver Operating Characteristics (ROC) curves

analysis. ROC curve is a plot of the true positive rate (sensitivity) versus the false positive rate (1-

specificity) for different thresholds over the entire range of each classifier output values. In

contrast with the classification accuracies obtained from truth tables, ROC analysis is independent

of class distribution or error costs. The best feature combination was considered the subset of

features that led to the highest – area under the ROC curve – value (AUC) with the LOO method.

The AUC can be statistically interpreted as the probability of the classifier to correctly classify

High from Low-Risk cases. In this study, the AUC is obtained by the binomial parametric method

in order to approximate the area. This method computes the AUC by fitting two normal

distributions to the data [197].

The hybrid multi-scale model and feature generation along with the design, training and testing of

both classifiers were all implemented in Matlab 6.5. The ROC analysis was made with the NCSS,

PASS and GESS software package. The computer used for processing had an AMD 64 Athlon

processor running at 3.6 GHz and 1.00 GB of RAM.

Chapter 10

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10.2 Results and Discussion

Two pattern recognition models (SVM and PNN) have been developed and utilized several

morphological and wavelet local maxima features for assessing the malignancy risk factor of

thyroid nodules. The classification experiments utilized the SVM (with the polynomial up to 4th

degree and RBF kernels) and PNN classifiers, in two independent feature sets. At first, the model

evaluation has been made in the feature set that was extracted from the wavelet local maxima that

corresponded only to significant structures. Afterwards the classifiers are also tested in the feature

set that incorporates the local maxima classified as speckle.

10.2.1 SVM & PNN Model Evaluation Without the Presence of Speckle

Table 10.2 reports the results of ROC analysis for both classifiers. AUC represents the probability

that a random pair of High and Low-Risk thyroid nodules will be correctly classified. Sensitivity

(SN) depends only on measurements of High-Risk nodules and specificity (SP) only on Low-Risk

nodules. The likelihood ratio measures the power of each classifier for increasing certainty about

a positive diagnosis.

Table 10.2 ROC analysis results of “Smoothness – Symmetry – Standard Deviation of Local

Maxima” feature combination for the SVM classifier and “Concavity – Fractal Dimension –

Standard Deviation of Local Maxima” for the PNN classifier in the speckle-free thyroid nodules


Confidence Limit)

Sensitivity (SN)

Specificity (SP)

Likelihood Ratio

SN/(1-SP)

Number of Support Vectors

SVM with Polynomial of 1st degree kernel

0.88 (0.69 – 0.96) 0.93 0.90 9.3 13

SVM with Polynomial of 2nd degree kernel

0.96 (0.84 – 0.99) 0.93 0.98 46.5 7

SVM with Polynomial of 3rd degree kernel

0.92 (0.78 – 0.97) 0.87 0.93 12.4 10

SVM with Polynomial of 4th degree kernel

0.89 (0.69 – 0.97 ) 0.93 0.93 13.3 12

SVM with RBF kernel 0.91 (0.79 – 0.96) 0.93 0.96 23.2 17

PNN 0.91 (0.85 – 0.95) 0.96 0.94 16

In the SVM model, highest classification accuracy with the minimum number of features (AUC –

0.96) by the LOO method was achieved by the feature combination “Smoothness – Symmetry –

Standard Deviation of Local Maxima”, employing the polynomial kernel of 2nd degree. This

combination gave sensitivity and specificity values of 0.93 and 0.98 respectively and a likelihood

ratio value of 46.5. In Figure 10.2(a), the binomial ROC curves of various kernels for the SVM

model with the best feature combination are depicted. The maximum classification accuracy


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coincides to the minimum number of support vectors involved in the design of the SVM

classifier.

Figure 10.2 Receiving Operating Characteristics (ROC) curves by the binomial method of (a)

SVM classifier with polynomial and RBF kernels employing the best feature combination and (b)

SVM with the 2nd degree polynomial kernel against PNN classifier for their corresponding best

feature combination in the speckle-free thyroid nodules

The number of support vectors for the best feature combination ranged from 8% to 20% of the

number of training points. Since the decision hyperplane of the SVM classifier is determined only

Chapter 10

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by the support vectors, their minimum number is indicative of the SVM low complexity and

differentiation capability. In Figure 10.3, we present the scatter diagram of the best feature

combination along with each class margins and the SVM (2nd degree polynomial) decision

boundary.

Figure 10.3 “Smoothness”, “Symmetry” and “Standard Deviation of Local Maxima” scatter

diagram, displaying the low-risk, high-risk and support vectors thyroid nodule data points along

with the SVM classifier (2nd degree polynomial kernel) decision boundary.

Regarding the PNN model, highest classification performance (AUC – 0.91) is accomplished

with the combination of “Concativity – Fractal Dimension – Standard Deviation of Local

Maxima” features. The PNN classifier exhibited relatively high performance in distinguishing


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Low from High-Risk thyroid nodules with 0.96 sensitivity and 0.94 specificity values giving a

likelihood ratio of 16. In Figure10.2(b) the SVM (2nd degree polynomial kernel) and the PNN

ROC curves by the binomial approach are illustrated. Regardless its smaller AUC value

compared to SVM with 3rd degree and RBF kernels the PNN classifier provides a tighter

confidence bound which in turn increases its power of separation. Figure 10.4 represents the

scatter diagram of high and low Risk thyroid nodules points with the PNN decision boundary

superimposed.

Figure 10.4 “Concavity”, “Fractal Dimension” and “Standard Deviation of Local Maxima”

scatter diagram, displaying the low and high-risk thyroid nodule data points and the PNN decision

boundary

Chapter 10

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A comparison between the two areas under the ROC curves (AUCsvm – AUCPNN) has also been

made so as to estimate whether two classifiers have significant difference. A significance level of

5% (0.05) is pre-selected as a criterion for a statistical difference. The AUC difference between

the two curves is equal to the criterion, hence the H0 is rejected, which suggests statistical

equivalence between the two classifiers. Obviously this decision due to marginal equivalence is

subjected to an error probability. Taking into account that the two classifiers are not statistically

different we can safely assume that all five features that comprise both best features combinations

exhibit high class separability power.

The irregularity degree, the non-circular boundary and the presence of micro-calcifications have

already been reported with relative high precision as suggestive of thyroid malignancy

[4,6,10,11]. However, these observations luck of certain and explicit patterns that could guide an

objective evaluation procedure. In this study the quantification of - until know - only observable

shape and texture characteristics has led to an extensive feature generation that encoded any

available information from each thyroid nodule.

Both SVM and PNN classifiers have seized the complicated relationship between the shape and

local maxima features towards an accurate differentiation between low and high-risk thyroid

nodules. The presence of small concave regions (concativity) and the increased irregularity

(smoothness) in the nodule’s boundary have been proved as significant characteristics that

suggest potential thyroid malignancy. Similarly, the noticeable difference between the nodule’s

width and length (symmetry) and the increased variability of MCs (LM Standard Deviation),

suggest potential malignancy. On the contrary, the lack of concave points, the regular borderline,

the round-like nodule shape and the undifferentiated aggregation of MCs coincide with

benignancy. The fact that features such as perimeter and area, which are associated with the size

of the nodule, exhibited poor differentiation performance is worth noticing.

The wavelet transform can detect discontinuities in the gray-level map with high precision.

Moreover, the computation and localization of local maxima from the wavelet coefficients

discloses not only the presence of a sudden abnormality but also the extent of this alteration by

employing its amplitude. The LM-based features introduced in this research can be considered as

equivalent to textural features. The echogenicity degree of a nodule can be comparable to the

number of LM inside the nodule. A small number of LM suggests the absence of structures within

the nodule, which can be fairly interpreted as hypo-echogenicity and not as iso or hyper-

echogenicity with almost zero gray level variability. The ratio (first order histogram) between the

number of local maxima and the total number of points within the nodule encodes such

echogenicity information.


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Furthermore, the differentiation degree of the LM amplitudes can be regarded as analogous to the

massive or scattered presence of MCs within the nodule. High variability stands for presence of

MCs scattered in rather hypoechogenic environment whereas low variability represents relatively

aggregated MCs in the same environment. Besides the concentration amount of MCs acquired

from the variability of LM amplitudes, additional information can be received in case of high

values of standard deviation. In such case, the nodule’s environment cannot be presumed only as

a whole hypo, iso or hyper echogenic but the co-existence of various echogenicity types within

the nodule may also be concluded.

An accessional advantage of the LM features is that both classifiers don’t acquire additional

processing time (for textural features computation) since the local maxima edge map is derived

directly from the hybrid multi-scale model that segments the nodules. The only information

related to LM that hasn’t quantified in this study is the degree of scattering, in terms of position

proximity, with respect to the nodule’s boundary. The integration of each local maximum

orientation in a future study might provide more information regarding the MCs positions.

10.2.2 SVM & PNN Model Evaluation With the Presence of Speckle

Table 10.3 provides the results of ROC analysis in the feature set wit speckle for both classifiers.

For the SVM classifier, best feature combination (AUC – 0.88) comprised the symmetry and

standard deviation of radius of the thyroid nodules boundaries, employing the polynomial kernel

of third degree.

Table 10.3 ROC analysis results of “Symmetry – Standard Deviation of Radius” feature

combination for the SVM classifier and “Concavity – Entropy of Radius” for the PNN classifier

in the thyroid nodules with speckle.


Confidence Limit)

Sensitivity (SN)

Specificity (SP)

Likelihood Ratio

SN/(1-SP)

Number of

Support Vectors

SVM with Polynomial of 1st degree kernel

0,83 (0,63 – 0,93) 0.74 0.90 7.4 11

SVM with Polynomial of 2nd degree kernel

0,86 (0,68 – 0,94) 0.74 0.91 8.3 11

SVM with Polynomial of 3rd degree kernel

0,88 (0,68 – 0,97) 0.93 0.96 23.2 10

SVM with Polynomial of 4th degree kernel

0,78 (0,52 – 0,86) 0.70 0.85 4.6 13

SVM with RBF kernel 0,79 (0,66 – 0,91) 0.74 0.87 5.6 13

PNN 0,86 (0,74 – 0,90) 0.84 0.88 7

Chapter 10

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The analogy (higher AUC – smaller number of support vectors) is also present in this particular

feature set. The binomial ROC curves for the SVM model for various kernels are depicted in

Figure10.5(a). The sensitivity and specificity values although reduced compared to the speckle-

free feature set remained high (0.93 and 0.96 respectively). However, the large confidence bound

indicates less discriminative power.

Figure 10.5 Receiving Operating Characteristics (ROC) curves by the binomial method of (a)

SVM classifier with polynomial and RBF kernels employing the best feature combination and (b)


- 138 -

SVM with the 3rd degree polynomial kernel against PNN classifier for their corresponding best

feature combination in the feature set with speckle.

Figure 10.6, describes the scatter diagram of the symmetry and standard deviation of radius for

the SVM (3rd degree) classifier along with its decision boundary, with the Re-Sub method.

Figure 10.6 “Symmetry” and “Standard Deviation of Radius” scatter diagram, displaying the

low-risk, high-risk and support vectors thyroid nodule data points along with the SVM classifier

(3rd degree polynomial kernel) decision boundary

The PNN classifier employed as best feature combination (AUC – 0.86) the concavity and radius

entropy of each nodule’s boundary. Its performance is degraded in the speckled feature set

achieving 0.84 and 0.88 sensitivity and specificity values. In Figure 10.5(b) the binomial ROC

curves of the SVM (3rd degree) against PNN classifiers are shown. It is worth noticing that the

PNN algorithm manages to retain the narrowest confidence interval compared to the SVM. Figure

10.7, describes the scatter diagram of concavity vs. radius entropy and the PNN decision

boundary with the Re-Sub method.

Chapter 10

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Figure 10.7. “Concavity” and “Entropy of Radius” scatter diagram, displaying the low and high

risk thyroid nodule data points and the PNN decision boundary

The impact, speckle had on the feature selection procedure towards the optimum combination

with the higher discriminatory score was greater than expected in the beginning of this study. The

classification power of both classifiers is reduced, whereas the utilization of features derived only

from the morphological group is an issue that requires further investigation. The decrement of the

feature number without a great reduction in overall precision can be considered as an important

asset on the algorithm complexity and power of SVM and PNN models. Nevertheless, it cannot

compensate for the removal of the important information the LM features provide (MC presence

or not and aggregation or not, etc) in the evaluation procedure of the nodule’s malignancy risk

factor. The literature is full with reports that acknowledge speckle’s deteriorating effect in the US

image quality. On the contrary, two reports [112,113] have been integrated speckle phenomenon

as a feature to improve classification of liver cirrhosis and breast cancer. All aforementioned

reports considered speckle as an overall natural phenomenon and did not attempt to quantify and

evaluate its influence. In this study, speckle has been correctly identified and localized in a


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microscopic pixel by pixel level (local maxima with negative Lipschtiz exponents) and for the

first time a parallel study has been held (with and without speckle) to evaluate its importance in

more details. In the original US image speckle effect cannot be easily evaluated however,

according to our study, in the LM feature level it had a negative influence.

10.3 Conclusion

A comprehensive study has been made that aimed at the generation of several morphological and

wavelet local maxima features and the design of two powerful classifiers (SVMs and PNN), in

order to evaluate the malignancy risk factor in ultrasound thyroid nodules. Moreover, a study on

the speckle effect in the classification procedure has been made. Various shape-based and LM

features proved to differentiate suspicious from benign nodules, such as concave regions,

borderline irregularity, shape asymmetry and presence of MCs. These features were well defined

and could be integrated in the overall diagnostic procedure. Another important conclusion of this

study was that speckle limited the performance of the classifiers due to subtraction of features

associated with MCs during the classification procedure.

The continuously growing amount of information, derived from the ultrasound image, has turned

the decision whether or not the patient must undergo into FNA as a rather complex procedure.

This fact constitutes pattern recognition algorithms as an essential auxiliary tool, in order to

parameterize and quantify all available information.

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CHAPTER 11

Conclusions and Future Perspectives

11.1 Conclusion

As a final conclusion we can say that an extensive study regarding image processing and analysis

methods has been made in thyroid ultrasonography. The study comprised from denoising and

segmentation algorithms to pattern recognition approaches such as SVMs, PNN and other

classical classifiers. Regarding the image processing techniques employed in this study, special

emphasis has been made in wavelet transform theory, whereas in image analysis methods, the

main classification models that have been designed and implemented were the SVMs and PNN.

In more details, the speckle phenomenon that dominates ultrasound imaging has been suppressed

by means of a wavelet-based speckle reduction algorithm. An inter-scale wavelet analysis has

been made towards edge detection and isolation edges across scales. Consequently, singularity

detection has been held in these edges in order to discriminate speckle from important image

features within the ultrasonic image. The success of the proposed method has been proven with

various indexes compared to several well-known speckle reduction algorithms. In addition a

clinical study has proven that the proposed algorithm can enhance the overall diagnostic

procedure.

Besides the speckle-suppression algorithm, within the same wavelet framework a new

segmentation hybrid algorithm has been introduced towards thyroid boundary detection. The

proposed model combined the wavelet transform, an inter-scale model and the constrained Hough

Transform to extract round-like objects from a rather noisy environment. The segmentation

method may assist in the thyroid nodule categorization from the physician based in morphology

characteristics.

The classification between high and low risk thyroid nodules has been made with various pattern

recognition algorithms that employed several textural, morphological and wavelet-based features.

The primary model through this study was the SVM that was accompanied with other models for

comparison reasons, such as the QB, LSMD, MLP, and PNN classifiers. Various textural features

have been proved to discriminate with relatively high accuracy the thyroid nodules, such as the

Sum Variance from the Co-Occurrence matrix, the gray-level mean value, the Run Length Non-

Uniformity from the run length matrices along with various shape features (i.e. concativity,

Conclusions and Future Perspectives

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roundness, fractal dimension etc). Moreover, a study on the speckle effect in the classification

procedure has been made. Two independent studies have been made that employed wavelet-based

features with and without the presence of speckle. The important conclusion of this study was that

speckle reduced the performance of the classifiers due to subtraction of wavelet-based features

associated with micro-calcifications during the classification procedure.

11.2 Future Work

The advent of new methods and algorithms necessitate the need for future work. The study held

in this thesis presents a number of points that require closer examination. The multiscale edge

representation (MER) procedure employed in both the despeckling and segmentation procedures

requires extra investigation. The employment of second derivative spline wavelets will alter not

only the way local maxima are located but possibly the algorithm’s performance. Moreover, new

and more efficient methods towards local maxima detection in the already implemented wavelet

framework could enhance the performance of the proposed methods. An important perspective is

the implementation of new approaches that could correlate the wavelet coefficients with various

image structures beside the local maxima presentation. The proposed hybrid model is highly

dependent on the local maxima detection and chaining in the first stage of the algorithm. The

employment of additional characteristics, beside the abrupt changes in the gray level, such as the

echogenicity difference between inside and outside the nodule and other features might improve

the algorithm’s performance even in cases that it proved unable to process. The time performance

for both algorithms is a critical issue. Due to MATLAB platform the processing time requires

several seconds either to denoise or to segment the ultrasound images. Computational time can be

decreased into sub-second time by exploiting the proposed algorithms with the C++ language

platform.

Regarding the pattern recognition methods employed in this study, emphasis must be given in

increasing the patient dataset in order to improve the generalization. Moreover, new acquisition

techniques such as DICOM archiving must be implemented so as to offer our clinical confirmed

database into other research groups and vise-versa.

The utilization of new and more efficient classifiers could improve the accuracy performance

towards thyroid nodule malignancy risk factor assessment. The features served as input into all

classifiers in this study has proven to posses high discriminatory attributes. However the

generation of more features, especially from the wavelet framework, may enhance the evaluation

procedure accuracy. Feature work could also involve the combination of texture, shape and

wavelet-based characterization methods towards segmentation and classification purposes.

143

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APPENDIX I

List of Figures Figure 2.1 The thyroid gland……………………………………………………………….. 9 Figure 2.2 Schematic representation of Hypothalamic - Pituitary - Thyroid axis…………. 10 Figure 2.3 Ultrasonographic examination in the transverse plane of the thyroid containing a solid nodule in the right lobe and a homogeneous appearance on the left lobe…………...

12

Figure 2.4 Scintiscans of thyroid. (a)The scan on the left is normal. (b) A typical scan of a "cold" thyroid nodule failing to accumulate iodide isotope is shown on the right………….

12

Figure 2.5 Classification of thyroid solitary nodules………………………………………. 13 Figure 2.6 (a) Thyroid nodule with epithelial hyperplasia, (b) Colloid nodule……………. 14 Figure 3.1 HDI-3000-ATL digital ultrasound system……………………………………… 17 Figure 3.2 US image of the thyroid gland with a cystic nodule……………………………. 17 Figure 3.3. Image processing system for acquisition and storage of US images…………... 19 Figure 4.1 One-dimensional – three level – redundant discrete dyadic wavelet transform... 25 Figure 4.2 (a) A cubic spline function and (b) a wavelet that is a quadratic spline of compact support……………………………………………………………………………..

27

Figure 4.3 Two dimensional – three level – redundant dyadic wavelet transform………… 29 Figure 4.4 Redudant dyadic wavelet transform of the Circle image………………………. 31 Figure 4.5 The gradient magnitude, the gradient directions and the local maxima of the Circle image…………………………………………………………………………………

33

Figure 5.1 (a),(b),(c),(d) Wavelet transform of f(t) calculated with quadratic spline wavelet ψ=-θ’ where θ is the cubic spline smoothing function approximating the Gaussian. The red stars are the local maxima of the wavelet coefficients along each scale. The scale increases from top to bottom. (e) Maxima line in the scale-space plane inside the cone of influence…………………………………………………………………………….

38

Figure 5.2 Wavelet transform of f(t) calculated with quadratic spline wavelet ψ=-θ’ where θ is the cubic spline smoothing function approximating the Gaussian. The red stars are the local maxima of the wavelet coefficients along each scale. The scale increases from top to bottom……………………………………………………………………………………….

40

Figure 5.3 The full line gives the decay of ),(log2 suWf from Figure (5.2) as a function of log2s along the maxima line that converges to the abscissa t=11. The dashed line gives

),(log2 suWf along the maxima line that converges at t=168……………………………..

41

Figure 6.1 (a) Image array with four grey levels. (b) General form of any grey-tone co-occurrence matrix. (c)-(f) Computation of all four co-occurrence matrices with distance d=1…………………………………………………………………………………………..

45

Figure 6.2 (a) Image array with four grey levels. (b)-(e) Computation of all four run length matrices for texture analysis…………………………………………………………. 48

List of Figures

- 158 -

Figure 6.3 Line segments used to compute radius…………………………………………. 50 Figure 6.4 Line segments used to compute Smoothness…………………………………… 51 Figure 6.5 Convex hull is used to compute concavity and concave points………………… 52 Figure 6.6 Line segments used to compute Symmetry. The lengths of perpendicular segments on the right of the major axis are compared to those on the left………………….

52

Figure 6.7 Fractal dimension estimation. N is the number of covering boxes and s is the number of ‘rules’ or the size (perimeter) of each box……………………………………….

53

Figure 6.8 Schematic diagram of the multilayer perceptron neural network employed, with two input features, two classes, two hidden layers and four nodes in each hidden layer………………………………………………………………………………………….

56 Figure 6.9 Schematic diagram of the probabilistic neural network employed, with two input features and two classes……………………………………………………………….

57

Figure 7.1 Block Diagram of the proposed wavelet based algorithm for speckle suppression…………………………………………………………………………………..

65

Figure 7.2 At the top is the original US image. The two columns show respectively the horizontal and vertical wavelet transform 31

2231

12 ),(,),( ≤≤≤≤ jj yxfWyxfW jj along three

dyadic scales. The scale increases from top to bottom……………………………………...

68 Figure 7.3 At the top is the original US image. The first column displays the modulus images ),(

2yxfM j . High intensity values correspond to black pixels whereas low

intensity values to white pixels for optimized visual interpretation of the results. At the second column the angle images ),(2 yxfA j are shown. The angle value turns from 0 (white) to 2π (black) along the circle contour. At the last column, the image points where

),(2

yxfM j has local maxima in the direction indicated by ),(2

yxfA j are presented (black pixels). Each time such a point is detected, the position of the resultant local maxima is recorded as well together with the values of the modulus ),(2 yxfM j and

angle ),(2 yxfA j at the corresponding locations…………………………………………...

70

Figure 7.4 Inter-scale back-propagation maxima connectivity in wavelet space…………... 73 Figure 7.5 At the first column are the wavelet transform modulus maxima (non-propagating maxima and propagating maxima with negative Lipschitz exponents) classified as speckle. In the second are the propagating maxima with positive Lipschitz exponents classified as important edges…………………………………………………….

74 Figure 7.6 (a) US image of the thyroid gland. (b) ASSF method, (c) wavelet shrinkage with soft thresholding, (d) wavelet shrinkage with hard thresholding, (e) wavelet inter-scale analysis denoising……………………………………………………………………..

77 Figure 7.7 Locally selected area containing the thyroid nodule – Box A for β calculation. Locally selected area corresponding to homogenous tissue – Box B for S/mse calculation...

78

Figure 7.8 The scan line including the borders (A&B) of the thyroid nodule……………... 78 Figure 7.9 Scan profiles of US thyroid image. High intensity line corresponds to the denoised scan line whereas low intensity line to original image. (a) ASSF method, (b) Soft thresholding, (c) hard thresholding, (d) wavelet inter-scale analysis denoising…………….

79 Figure 7.10 (a) Original US image, (b) De-speckled US image…………………………… 80

Appendix I

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Figure 7.11 (a) Original US image, (b) De-speckled US image…………………………… 80 Figure 7.12 (a) Original US image, (b) De-speckled US image…………………………… 80 Figure 7.13 Microsoft access interface employing the questionnaire for US images denoising evaluation…………………………………………………………………………

81

Figure 8.1 Schematic representation of the segmentation algorithm………………………. 93 Figure 8.2 Local maxima linking procedure. Adjacent local maxima form a maxima chain

kjC,2

due to positional proximity combined with amplitude and angle values similarity…..

97

Figure 8.3 (a) Synthetic Image, (b) Hough parameter space via projecting circles with variable radius. High amplitude values (candidate center points) correspond to white pixels, (c) Accumulator array, (d) Segmented image………………………………………..

101 Figure 8.4 (a) US image with an iso-echoic thyroid nodule, (b) Contour representation, (c) Constrained Hough transform, (d) Accumulator array, (e) Outcome of the hybrid model, (f) Manually delineated boundary…………………………………………………………...

104 Figure 8.5 (a) US image with a hypo-echoic thyroid nodule, (b) Contour representation, (c) Constrained Hough transform, (d) Accumulator array, (e) Outcome of the hybrid model, (f) Manually delineated boundary…………………………………………………...

105 Figure 9.1 “Sum variance” versus “mean gray value” scatter diagram, displaying the low-risk and high-risk thyroid nodule data points, the SVM classifier margins, and the decision boundary employing the polynomial kernel of 3rd degree…………………………………..

118 Figure 9.2 “mean gray value”, and “run length non-uniformity” scatter diagram, displaying the low-risk and high-risk thyroid nodule data points and the MLP classifier decision boundary…………………………………………………………………………...

119 Figure 9.3 “Sum variance”, “mean gray value”, and “run length non-uniformity” scatter diagram, displaying the low-risk and high-risk thyroid nodule data points and the QB classifier decision boundary…………………………………………………………………

121 Figure 9.4 “Sum variance”, “mean gray value”, and “run length non-uniformity” scatter diagram, displaying the low-risk and high-risk thyroid nodule data points and the QLSMD classifier decision boundary…………………………………………………………………

122 Figure 9.5 “Sum variance” versus “mean gray value” scatter diagram, displaying the low-risk and high risk thyroid nodule data points, the SVM classifier margins, and the decision boundary employing the Daubechies wavelet kernel………………………………………..

124 Figure 9.6 “Sum variance” versus “mean gray value” scatter diagram, displaying the low-risk and high risk thyroid nodule data points, the SVM classifier margins, and the decision boundary employing the Coiflet wavelet kernel…………………………………………….

125 Figure 9.7 “Sum variance” versus “mean gray value” scatter diagram, displaying the low-risk and high-risk thyroid nodule data points, the SVM classifier margins, and the decision boundary employing the Symmlet wavelet kernel…………………………………………..

126 Figure 10.1 US images representing various morphologic types of Low-Risk and High-Risk Thryoid nodules………………………………………………………………………. 128 Figure 10.2 Receiving Operating Characteristics (ROC) curves by the binomial method of (a) SVM classifier with polynomial and RBF kernels employing the best feature combination and (b) SVM with the 2nd degree polynomial kernel against PNN classifier for their corresponding best feature combination in the speckle-free thyroid nodules……. 132

List of Figures

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Figure 10.3 “Smoothness”, “Symmetry” and “Standard Deviation of Local Maxima” scatter diagram, displaying the low-risk, high-risk and support vectors thyroid nodule data points along with the SVM classifier (2nd degree polynomial kernel) decision boundary…..

133 Figure 10.4 “Concativity”, “Fractal Dimension” and “Standard Deviation of Local Maxima” scatter diagram, displaying the low and high-risk thyroid nodule data points and the PNN decision boundary…………………………………………………………………

134 Figure 10.5 Receiving Operating Characteristics (ROC) curves by the binomial method of (a) SVM classifier with polynomial and RBF kernels employing the best feature combination and (b) SVM with the 3rd degree polynomial kernel against PNN classifier for their corresponding best feature combination in the feature set with speckle………….

137

Figure 10.6 “Symmetry” and “Standard Deviation of Radius” scatter diagram, displaying the low-risk, high-risk and support vectors thyroid nodule data points along with the SVM classifier (2nd degree polynomial kernel) decision boundary………………………………..

138 Figure 10.7 “Concativity” and “Entropy of Radius” scatter diagram, displaying the low and high risk thyroid nodule data points and the PNN decision boundary…………………. 139

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APPENDIX II

List of Tables Table 7.1 Image quality measures obtained by four denoising methods tested on a digital ultrasound phantom image…………………………………………………………………..

76

Table 7.2 Image quality measures obtained by four denoising methods tested on an ultrasound image of the thyroid gland………………………………………………………

78

Table 7.3 1st Observer’s evaluation of algorithm performance…………………………….. 82 Table 7.4 2nd Observer’s evaluation of algorithm performance……………………………. 83 Table 7.5 Observers evaluation of algorithm performance………………………………… 84 Table 7.6 Agreement (kappa coefficient) between the two observers……………………... 85 Table 8.1 Percentage agreement between automatic (AU) and manual segmentations (OB1, OB2) in terms of Area, Roundness, Concavity and MAD%..........................................

103

Table 8.2 Mean values and standard deviation of the computed MADs for the pairs AU – OB1 and AU – OB2…………………………………………………………………………..

103

Table 8.3 Inter-observer agreement (kappa coefficient) between the two observers………. 106 Table 9.1. Classification accuracies for various SVM kernels using the leave-one-out and re-substitution methods, for the “mean gray value – sum variance” best feature combination………………………………………………………………………………….

116 Table 9.2. Truth table of the SVM classifier employing the 3rd degree polynomial kernel, and the “mean gray value – sum variance” best feature combination………………………

117

Table 9.3. Truth table of the MLP classifier employing he “mean gray value – Run Length Non Uniformity” best feature combination…………………………………………

119

Table 9.4. Truth table of the QLSMD classifier employing the “mean gray value – sum variance – run length non-uniformity” best feature combination…………………………...

120

Table 9.5. Truth table of the QB classifier employing the “mean gray value – sum variance – run length non-uniformity” best feature combination…………………………...

120

Table 9.6. Classification accuracies for various SVM wavelet kernels using the leave-one-out and re-substitution methods, for the “mean gray value – sum variance” best feature combination………………………………………………………………………………….

123 Table 9.7. Truth table of the SVM classifier with the Daubechies wavelet kernel employing the “mean gray value – sum variance best feature combination………………...

123

Table 9.8. Truth table of the SVM classifier with the Coiflet wavelet kernel employing the “mean gray value – sum variance best feature combination………………………………...

123

Table 9.9. Truth table of the SVM classifier with the Symmlet wavelet kernel employing

List of Tables

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the “mean gray value – sum variance best feature combination……………………………. 124 Table 10.1 Morphological and Local Maxima Features of Thyroid Nodules……………… 129 Table 10.2 ROC analysis results of “Smoothness – Symmetry – Standard Deviation of Local Maxima” feature combination for the SVM classifier and “Concavity – Fractal Dimension – Standard Deviation of Local Maxima” for the PNN classifier in the speckle-free thyroid nodules………………………………………………………………………….

131 Table 10.3 ROC analysis results of “Symmetry – Standard Deviation of Radius” feature combination for the SVM classifier and “Concavity – Entropy of Radius” for the PNN classifier in the thyroid nodules with speckle.………………………………………………

136

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APPENDIX III

List of Abbreviations

ASM: Angular Second Moment

ASSF: Adaptive Speckle Suppression Filter

B – Mode: Brightness Modulation

CV: Convex Hull

CWT: Continuous Wavelet Transform

D – Mode: Doppler Modulation

DWT: Dyadic Wavelet Transform

FD: Fractal Dimension

FNA: Fine Needle Aspirate

GLNU: Gray Level NonUniformity

GLRL: Gray Level Run Length

HT: Hough Transform

LM: Local Maxima

LOO: Leave One Out

LSMD: Least Square Minimum Distance

LVQ: Learning Vector Quintizer

M – Mode: Motion Modulation

MAD: Mean Absolute Distance

MD: Minimum Distance

MER: Multiscale Edge Representation

MLP: Multilayer Perceptron Network

MM: Modulus Maxima

NN: Neural Network

PDF: Probability Density Function

PNN: Probabilistic Neural Network

QB: Quadratic Bayesian

QP: Quadratic Programming

RBF: Radial Basis Function Network

List of Abbreviations

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RBR: Radial Bas-Relief

RDWT: Redudant Dyadic Wavelet Transform

Re-Sub:Re Substitution

RF: Radio Frequency

RKHS: Reproducing Kernel Hilbert Space

RLNU: Run Length Non Uniformity

ROI: Region Of Interest

RP: Run Percentage

S/mse: signal-to-mean-square-error ratio

SAR: Synthetic Aperture Radar

SI: Speckle Index

SRE: Sort Run Emphasis

SRM: Structural Risk Minimization

SV: Support Vector

SVAR: Sum Variance

SVM: Suppor Vector Machines

TGC: Time Gain Compensation

TRH: Thyrotropin Releasing Hormone

TSH: Thyroid Stimulating Hormone

US: ultrasonography

WT: Wavelet Transform

WTMM: Wavelet Trasnform Modulus Maxima

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APPENDIX IV Index of Terms

a trous 26,65,67,92 Discriminant function – PNN 56 Absolute distance 101 Discriminant function – QLSMD 54 Absorption 15 Doppler Modulation 16 Adaptive Speckle Suppression Filter 61,75,76 DWT 7,21,23,24,25,28 31,32,62,67,69,75,90,94 Anaplastic 13,14 Entropy 46,118,129 Angular second moment 46 Epithelial hyperplasia1 4,111,128 Back Propagation 72,73,75,85,92,96,113 Euclidean distance 50,52,54,101 Bayes 55,56,113 Feature extraction 22,43,68,96,127,128 Bayes - Decision Theory 55, 113 Feature selection 7,129,139 Bayes – Rule 56 Feature vector 54,55,57,113,116,129 Bayesian classifier 55,109,113 Fine needle aspiration 2,11,13,128,139 Biorthogonal wavelet 67 First order features 44 Boundary detection 1,4,87,89,92,103 Fractal dimension 53,128,132,133 Brightness Modulation 16 Frame grabber 18,19,94,111 Center of mass 51,100,101,132 Gaussian 27,32,38,39,40,65,67,98 Central moment 129 Gland 9,10,11,16,61,64,67,76,78,81,85,109 Chaining 72,98,107,108,142 Gradient Vector 32,33,65,69,91,94 Classification 13,43, 58,69, 95, 110,116,117,123 Gray Level Non Uniformity 49 Classification error 58,111,129 Hilbert space 109,114,115,126 Coherent 65 Hough Transform 4,87,92,99,100,104,106,107 Coiflet 114,123,124,125 Hyperthyroidism 10,109 Colloid nodule 2,13,14,111,128 Hypothyroidism 10 Cone of influence 37,38,39 Kernel Function 59,113,114,116,126 Continuous Wavelet Transform 21,22,23 Kurtosis 45,129 Contrast 3,46,64,81 Lagrangian 58 Convex Hull 51,52,102,129,132 Lagrangian – Dual 59 Convolution 21,23,28,32,67 Lagrangian – Primal 59 Co-Occurrence 45,46,47,111,112,141 Learning Vector Quintizer 62 Covariance matrix 55,113 Least Square Minimum Distance 109,112,120141 Cubic spline 27,38,40,67 Leave One Out 54,111,116,119,130,136 Daubechies 63,75,114,123,124,125 Linear transducer 16,17,64,94 Decision boundary 117,119,126,131,133,137,138 Lipschitz exponent 3,35,41,64,71,73,92 Decision rule 56 Local Maxima 3,32,37,44,69, 95,100,107,128, 142 Derivative 26,27,30,32,36,38,67,88,98,142 Long run emphasis 49 Diameter 52,76,130 Mallat 3,24,25,26,27,29,36,62,72 Discriminant function – Bayesian 55 Mean Absolute Distance 101 Discriminant function – MLP 56 Medullary 13,14

Index of Terms

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Mercer 59,115,126 Roundness 51,101,102,103,106,128,142 Mercer – Kernel 115 Run length 48,111,112 Minimum Distance 4,54,109,113 Run Length Non Uniformity 49,120 Modulus Maxima 3,32,35,39,64,69,73,92,95,128 Run Percentage 49 Moments 36,122,123 Scattering 15,16,135 Morphological features 4,12,127,128,129,139 Shift invariant 22,30,68 (MLP) network 4,55,56,109,111,112,113,119 Signal-to-mean-square-error ratio 75 Multiresolution 2,21,90 Singularity 35,36,38,41,65,75,85,95,106,141 Multiscale edge representation 32,94,95,96,142 Skewness 45,129 Neural Network 4,55,56,57,88,113 Short Run Emphasis 49 Normalization 53,54 Speckle 1,3,4,61,62,65,71,81,85,107,128,136 Pal (resolution) 19 Speckle Index 75 Parzen 56 Sum Variance 47,112,116,118,124 Pattern recognition 43,55,65,110,113,127,140 Support Vector 59,113,117,126 PNN 4,7,56,57,127,130,132,135,137,141 Symmlet 114,123,124,126 Probability Density Function 63 Synthetic Aperture Radar 63,85 Quadratic Bayesian 4,109,113 Thresholding 62,63,72,75,76,86 Quadratic spline 4,27,38,40,98 Thresholding – Hard 62,75,76 Radial Basis Function 113,114 Thresholding – Soft 62,75,76,86 Re Substitution 116,117,119,129,123,129,136,138 Thyroid Scan 12 Reflection 15,16,65 Thyroid Stimulating Hormone 9 Refraction 15 Thyrotropin Releasing Hormone 9 Region Of Interest 87,88,89,91,99,107,111,127 Thyroxine 9 Regularity 42,64,71,73,85,95,107,127 Time Gain Compensation 6,127 Reproducing kernel 114,115 Triiodothyronine 9 Reproducing Kernel Hilbert Space 109,114,126

phd stavros tsantis

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