microcalcification enhancement in digital mammogram

Microcalcification Enhancementin digital mammogramMasters -2 Work-progress Presentation #1

Nashid AlamRegistration No: 2012321028annanya_cse@yahoo.co.uk

Supervisor: Prof. Dr. M. Shahidur Rahman

Department of Computer Science And Engineering

Shahjalal University of Science and TechnologyWednesday, September 3, 2014

“The best protection is early detection”

Introduction

Breast cancer:The most devastating and deadly diseases for women.

o Computer aided detection (CADe) o Computer aided diagnosis (CADx) systems

Computerize Breast cancer Detection System:

Steps to control breast cancer:1) Prevention2) Detection3) Diagnosis4) Treatment

We will emphasis on :1) Detection2) Diagnosis

Micro-calcification

Mammography

Mammogram

Micro-calcification

Micro-calcifications :- Tiny deposits of calcium- May be benign or malignant- A first cue of cancer.

Position:1. Can be scattered throughout the mammary gland, or 2. Occur in clusters.(diameters from some µm up to approximately 200 µm [4].)

3. considered regions of high frequency.

They are caused by a number of reasons:

Aging - The majority of diagnoses are made in women over 50

Genetic - Involving the BRCA1 (breast cancer 1, early onset) andBRCA2 (breast cancer 2, early onset) genes

Mammography

USE:I. Viewing x-ray imageII. Manipulate X-ray image on a computer screen

Mammography :

Process of using low-energyx-rays to examine the human breast

Used as a diagnostic and a screening tool.

The goal of mammography :The early detection of breast cancer

Mammography Machine

Mammogram

Mammogram:A mammogram is an x-ray picture of the breast

Use:To look for changes that are not normal.

Result Archive:The results are recorded on x-ray film or directly into a computer

Types of mammograms:

I. Screening mammograms-Done for women who have no symptoms of breast cancer.

II. Diagnostic mammograms -To check for breast cancer after a lump or other symptom or sign of breast cancer has been found.

III. Digital mammogram-Uses x-rays to produce an image of the breast. The image is stored directly on a computer.

mdb226.jpg

Problem Statement

Main challenge :QUICKLY AND ACCURATELY overcome the development of breast cancer

Problem Statement

Reason behind the problem:Burdensome Task Of Radiologist :

Eye fatigueHuge volume of images

Detection accuracy rate tends to decreaseNon-systematic search patterns of humansPerformance gap between :

Specialized breast imagers andgeneral radiologists

Interpretational Errors:Similar characteristics:

Abnormal and normal microcalcification

Problem Statement

The signs of breast cancer are: Masses CalcificationsTumorLesionLump

Individual Research Areas

A key area of research activity involves :Developing better ways-

To diagnose and stage breast cancer.

• Develop a logistic model:

• Early detection of Breast Cancer.

-Micro-calcification detection

-To determine the likelihood of CANCEROUS AREA

from the image values of mammograms.

The Micro-calcification:Occur in clusters

The clusters may vary in size from 0.05mm to 1mm in diameter.

Variation in signal intensity and contrast.May located in dense tissue

Difficult to detect.

Why our work is important?

-Better Cancer Survival Rates(Early Detection ).

-The diagnostic management of breast cancer (a difficulttask)

--Radiologist fails to detect Breast Cancer.

-Computerized decision support systems provide“second opinion” :

Fast,Reliable, andCost-effective

Strickland et.at (1996) :A biorthogonal filter bank is used

-To compute four dyadic and -Two cinterpolation scales.

A binary threshold-operator is applied to the six scales.

Literature Review

Laine et.al (1994) :A hexagonal wavelet transform (HWT) is used:

-To obtain multi-scales edges at orientations of 60, 0 and -60 degrees.

The resulting subbands are enhanced and The image reconstructed.

Literature Review

Wang et.al.(1989):The mammograms are:

-Decomposed into different frequency subbands.

The low-frequency subband discarded.

The image is reconstructed from the subbands containing only high frequencies.

Literature Review

Heinlein et.al(2003):For general enhancement of mammograms:

From a model of microcalcifications -The integrated wavelets are derived

Literature Review

Zhibo et.al.(2007):A method aimed at minimizing image noise.

Optimize contrast of mammographic image featuresEmphasize mammographic features:

A nonlinear mapping function is applied:-To the set of coefficient from each level.

Use Contourlets:For more accurate detection of microcalcification clusters

The transformed image is denoised-using stein's thresholding [18].

The results presented correspond to the enhancement of regions with large masses only.

Literature Review

Fatemeh et.al.(2007) :

Focus on:

-Analysis of large masses instead of microcalcifications.

- Detect /Classify mammograms:

Normal and Abnormal

Use Contourlets Transform:

For automatic mass classification

Literature Review

Daubechies I.(1992): Wavelets are mainly used :

-Because of their dilation and translation properties-Suitable for non stationary signals.

Main Novelty

- Nonsubsampled Contourlet Transform

- Specific Edge Filter :To enhance the directional structures of the image in

the contourlet domain.

- Recover an approximation of the mammogram (with the microcalcifications enhanced):

Inverse contourlet transform is applied

Details in upcoming slides

Achievement

The proposed method

Outperforms

The current method

Contourlet transformation(CT)

based on:

Discrete wavelet transform(DWT)

based on:

Contourlet transformation

Implementation Based On :

• A Laplacian Pyramid decomposition followed by -

• directional filter banks applied on each band pass sub-band.

The non-subsampled contourlet transform extracts:• the geometric information of images.•which can be used to distinguish noises from weak edges.

Why Contourlet?

•Decompose the mammographic image into well localized and

directional components:

To easily capture the geometry of the image features.

•Accomplished by the 2-D Contourlet Transform (2D-CT) :

Improves the representation scarcity of images over the Discrete DWT [11], [12],[13], [14].

Target:

• This decomposition offers:-Multiscale and time frequency localization and -A high degree of directionality and anisotropy.

Usefulness of Conterlet :

Why Contourlet?

2-D Contourlet Transform (2D-CT) Discrete DWT

Handles singularities such as edges in a more powerful way

Has basis functions at many orientations has basis functions at three orientations

Basis functions appear a several aspectratios

the aspect ratio of WT is 1

CT similar as DWT can beimplemented using iterative filter banks.

Advantage of using 2D-CT over DWT:

Wavelet

Good temper resolution in high frequencies

Good frequency resolution in low pass band

OBTAION:

Wavelet

A high pass filter

Temper resolution : A vertical high-resolutionFrequency resolution : The sample frequency divided by the number of samples

O/P of Low Pass Filter High Pass Filter = A Band Pass Result

Wavelet

Working with wavelet:1. Convolve the signal with wavelet filter(h/g)2. Store the results in coefficients/frequency response

(Result in number is put in the boxes)3. Coefficients/frequency response:

- The representation of the signal in the new domain.

Properties:• Maximum frequency depends on the length of the signal.• Recursive partitioning of the lowest band in subjective to the application.

1.A length 8 signal

3.Convolve the signal with the high pass filter

2.Split/divide the signal in two parts

Wavelet

To avoid redundancy

Down sample by 2

Wavelet

• For perfect low pass filter• Leave everything intact in 0 (zero)

Spectrodensity of the signal at this point

Unit cell

Unit cell is shrunk by half(1/2)

Wavelet

No information loss due to shrinking

First partitioning of lower and higher frequency band

Wavelet

Spectrodensity of the signal at this point

For perfect low pass filter For perfect high pass filter

This works even not for perfect high pass/low pass filter

Wavelet

Split the signalAnd

down-sample by 2In high frequency

Details at level 1

Wavelet

Split inthe low frequency

Details at level 2

Wavelet

Extra Split inthe low frequency

Details at level 3

Wavelet

Approximationat level 3

Wavelet

Works for Signals of 8 samples

23= 8, Sample=8, level=3.

Wavelet

Positive half of the

frequency axis

1 2 3 4

Wavelet

Positive half of the

frequency axis

1 2 3 4

Wavelet

Positive half

the frequency axis

1 2 3 4

Wavelet

Positive half

the frequency axis

Details at level 2

Details at level 3

Detailsat

level 1

Approximation

Wavelet

Filter response/Coefficientof

perfect bandpass filter

Wavelet Behaving

as bandpass

Wavelet

Practically used wavelet filter

Collect the low frequencies

High frequencies

Wavelet Behaving

as bandpass

Wavelet

Practically used wavelet filter

Modular square ofThese transfer

function Add up to 1.

Prevent Loosing

signal/energy

Wavelet Behaving

as bandpass

Code Fragments to do the task

% Extract the level 1 coefficients.

a1 = appcoef2(wc,s,wname,1);

h1 = detcoef2('h',wc,s,1);

v1 = detcoef2('v',wc,s,1);

d1 = detcoef2('d',wc,s,1);

% Display the decomposition up to level 1 only. ncolors = size(map,1); % Number of colors.

sz = size(X);

cod_a1 = wcodemat(a1,ncolors);

cod_a1 = wkeep(cod_a1, sz/2);

cod_h1 = wcodemat(h1,ncolors);

cod_h1 = wkeep(cod_h1, sz/2);

cod_v1 = wcodemat(v1,ncolors);

cod_v1 = wkeep(cod_v1, sz/2);

cod_d1 = wcodemat(d1,ncolors);

cod_d1 = wkeep(cod_d1, sz/2);

image([cod_a1,cod_h1;cod_v1,cod_d1]);

axis image; set(gca,'XTick',[],'YTick',[]);

title('Single stage decomposition')

colormap(map)

% Here are the reconstructed branches

ra2 = wrcoef2('a',wc,s,wname,2);

rh2 = wrcoef2('h',wc,s,wname,2);

rv2 = wrcoef2('v',wc,s,wname,2);

rd2 = wrcoef2('d',wc,s,wname,2);

Wavelet

Transfer function of

The wavelets

Transfer function of

The Scaling function

Wavelet

Want to understand The effect of this label

Have to perform convolution

Understand The effect of each this label

Wavelet

Graph 01: Transfer functions of the wavelet transforms

Works for Signals more then 8 samples 23= 8, Sample=8, level=3.

Level 1details

Level 2details

Level 3details

Level 4details

Level 5details

Transfer functions of

Approximation:The low pass

result That we keep at

the end

Wavelet

Graph 01: Transfer functions of the wavelet transforms

Leveldetails

+ approximation= 1

Property of wavelet

Wavelet

Approximation is a sinc- A perfect low pass filter

sincA-sincBA=A frequencyB=A frequency

-A perfect bandpass filter

Wavelet

Signal withmore than

eight samplesScenario:

Temper resolution : A vertical high-resolutionFrequency resolution : The sample frequency divided by the number of samples

Temper resolution>Frequency resolution

Increasingfrequency resolution

Decreasestemporal resolution.

Discrete Wavelet Transform(DWT)

Requires a wavelet ,Ψ(t), such that:- It scales and shifts

from an orthonormal basis of the square integral function.

)2/)2((2

1)(, jt

Scale Shift

Denote Wavelet

j and n both are integer

nmjlmlnj ., ,, To offer an orthonormal basis:)(, tnj

Orthonormal basis: A vector space basis for the space it spans.

Basis Function

Wavelets,ΨBasis function : An element of a particular basis for a function space

Scaling Function,Ψ

With each label:By shifting-

Inter-product is zero

Wavelets are orthogonal

Details at level 1 Scale factor , j =2, 22 =4

Details at level 2

Scale factor , j =1, 21 =2

Details at level 3

Scale factor , j =0, 20 =1

ApproximationLow

frequency

No Scale factor

Daubchies’ Wavelet (DW)

•H()=high pass filter•D4=Daubchies’ Tap 4 Filter•Not symmetrical

Initial shape

Backward transformation of Wavelets

Opposite of forward transformationMirror the forward transformation on the right hand sideReplace the down-sampling by up-sampling.

Signal

Wavelettransform

of the Signal

Wavelettransform

of the Signal

Signal

Perfect step edge

JPEG Compression

15% lowestFourier coefficient=

Lowest 15 frequencyIs used to reconstruct the signal

Gibbs oscillation

Low pass version of the original image

JPEG Compression

15% largest scaleDaubchie’s coefficient=

JPEG Compression

Original signal

Wavelet coefficient(Symmlet wavelet)

ReconstructedThe 15% most important

coefficient=Getting fine output image

2D Wavelet Transform

Scaling function Wavelet

2Πk1 =ω1

2Πk2 =ω2

Low pass filter

High pass filter

WaveletWavelet

Use Separable Transform

Originalimage

hx = High pass filter(X-direction)

gx = low pass filter(X-direction)

hxy = High pass filter(y-direction)

gy = low pass filter(y-direction)

Further split

hy = High pass filter(y-direction)

hy = Low pass filter(y-direction)

Four region:

Blue= Diagonal Details at label 1

Green=Horizontal Details at label 1

Purple=vertical details at label 1

Yellow= Approximation at Label 1(Low pass in both x and y direction)

Doing the above steps recursively:Take the current approximation

Doing the above steps recursively:1. Take the current approximation2. And further split it up

New approximation

Doing the above steps recursively:1. Take the current approximation2. And further split it up3. Getting new approximation

Diagonal Details

Horizontal Details

vertical details

Approximation(can be furtherdecomposed)

In summary

Approximation(can be furtherdecomposed)

Visualization

Label ofapproximation

HorizontalDetails

VerticalDetails

DiagonalDetails

VerticalDetails

DiagonalDetails

VisualizationLabel of approximation:• Very strong low pass filter• Few pixels

Visualization

Details in

Various Scale

Visualization

vertical details ->Shoulder

Horizontal Details ->Edges

Diagonal Details

Visualization

# of occurrences

Magnitudeof

coefficients

MostCoefficientHave valuesClose to zero

Graph from the histogram

# of occurrences

Magnitudeof

coefficients

DiscardCoefficient

valuesClose to zero

More precise

Visualization

Original image:Gray square on a Black Background

Diagonal Details

Horizontal Details(row by row)

Vertical details(column by column)

Toy of original image

Decomposition at Label 4

Original image

Original image(with diagonal details areas indicated)

Diagonal Details

Vertical Details

Original image(with Vertical details areas indicated)

Experimental Results

1.Original Image(Malignent_mdb238) 2.Decomposition at Label 4

2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3

1.Original Image(Malignent_mdb238) 2.Decomposition at Label 4

1.Original Image(Benign_mdb252)

2.Decomposition at Label 4

1.Original Image(Malignent_mdb253.jpg) 2.Decomposition at Label 4

CT vs. DWT

DWT Target Goal:1.Applying a DWT to decompose a digital mammogram into different subbands.

2.The low-pass wavelet band is removed (set to zero) and the remaining coefficients are enhanced.

3.The inverse wavelet transform is applied to recoverthe enhanced mammogram containing microcalcifications [7].

7. Wang T. C and Karayiannis N. B.: Detection of Microcalcifications in Digital Mammograms Using Wavelets, IEEETransaction on Medical Imaging, vol. 17, no. 4, (1989) pp. 498-509

The results obtained by the Contourlet Transformation (CT)are compared with

The well-known method based on the discrete wavelet transform

Plan-of-Action

For microcalcifications enhancement :

We use-The Nonsubsampled Contourlet Transform(NSCT) [12]

The Prewitt Filter.

12. Da Cunha A. L., Zhou J. and Do M. N,: The Nonsubsampled Contourlet Transform: Theory, Design, and

Applications, IEEE Transactions on Image Processing,vol. 15, (2006) pp. 3089-3101

Plan-of-Action

An edge Prewitt

filter to enhance the

directional structures

in the image.

Contourlet transform allows

decomposing the image in

multidirectional

and multiscale subbands[6].

6. Laine A.F., Schuler S., Fan J., Huda W.: Mammographic feature enhancement by multiscale

analysis, IEEE Transactions on Medical Imaging, 1994, vol. 13, no. 4,(1994) pp. 7250-7260

This allows finding • A better set of edges,• Recovering an enhanced mammogram with better visual characteristics.

microcalcifications have a very small size a denoising stage is not implemented

in order to preserve the integrity of the injuries.

Decompose the

digital mammogram

Contourlet transform

(b) Enhanced image(mdb238.jpg)

(a) Original image (mdb238.jpg)

Method

The proposed method is based on the classical approach used in transform

methods for image processing.

1. Input mammogram

2. Forward NSCT

3. Subband Processing

4. Inverse NSCT

5. Enhanced Mammogram

Figure 01: Block diagram of the transform methods for images processing.

Method

NSCT is implemented in two stages:

1. Subband decomposition stage

2. Directional decomposition stages.

Method

For the subband decomposition:- The Laplacian pyramid is used [13]

Decomposition at each step:-Generates a sampled low pass version of the original-The difference between :

The original image and the prediction.

13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank for image analysis and classification,Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp.1417-1420

Details ……..

Method

Details ……..

1. The input image is first low pass filtered

2. Filtered image is then decimated to get a coarse(rough) approximation.

3. The resulting image is interpolated and passed through a Synthesis

flter.

4. The obtained image is subtracted from the original image :

To get a bandpass image.

5. The process is then iterated on the coarser version (high resolution)of the image.

Plan of Action

Method

2.Directional Filter Bank (DFB)

Details ……..

Implemented by using an L-level binary tree decomposition :

resulting in 2L subbands

The desired frequency partitioning is obtained by :

Following a tree expanding rule

- For finer directional subbands [13].

13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank for image analysis and classification,Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp.1417-1420

The Contourlet Transform

The CT is implemented by:Laplacian pyramid followed by directional filter banks (Fig-01)

Input image

Bandpass

Directional

subbands

Bandpass

Directional

subbands

Figure 01: Structure of the Laplacian pyramid together with the directional filter bank

The concept of wavelet:University of Heidelburg

The CASCADE STRUCTURE allows:- The multiscale and

directional decomposition to be independent

- Makes possible to:Decompose each scale into

any arbitrary power of two's number of directions(4,8,16…)

Figure 01

Details ………….

Decomposes The Image Into Several Directional Subbands And Multiple Scales

Figure 01: (a)Structure of the Laplacian pyramid together with the directional filter bank(b) frequency partitioning by the contourlet transform(c) Decomposition levels and directions.

(a) (b)

Bandpass

Directional

subbands

Bandpass

Directional

subbands

Details….

DenoteEach subband by yi,j

Wherei =decomposition level and J=direction

Decomposes The Image Into Several Directional Subbands And Multiple Scales

The processing of an image consists on:-Applying a function to enhance the regions of interest.

In multiscale analysis:

Calculating function f for each subband :

-To emphasize the features of interest

-In order to get a new set y' of enhanced subbands:

Each of the resulting enhanced subbands can be

expressed using equation 1.

)(', , jiyfjiy ………………..(1)

-After the enhanced subbands are obtained, the inverse

transform is performed to obtain an enhanced image.

Enhancement of the Directional Subbands

Denote

Each subband by yi,jWherei =decomposition level and J=direction Details….

Details….

The directional subbands are enhanced using equation 2.

)( , jiyf)2,1(

,1 nnWjiy

)2,1(,2 nnWjiy

If bi,j(n1,n2)=0

If bi,j(n1,n2)=1………..(2)

Denote

Each subband by yi,jWherei =decomposition level and J=direction

W1= weight factors for detecting the surrounding tissueW2= weight factors for detecting microcalcifications

(n1,n2) are the spatial coordinates.

bi;j = a binary image containing the edges of the subband

Weight and threshold selection techniques are presented on upcoming slides

The directional subbands are enhanced using equation 2.

)( , jiyf)2,1(

,1 nnWjiy

)2,1(,2 nnWjiy

If bi,j(n1,n2)=0

If bi,j(n1,n2)=1………..(2)

Binary edge image bi,j is obtained :-by applying an operator (prewitt edge detector)

-to detect edges on each directional subband.

In order to obtain a binary image:A threshold Ti,j for each subband is calculated.

Details….

Weight and threshold selection techniques are presented on upcoming slides

Threshold Selection

Details….

In order to obtain a binary image:A threshold Ti,j for each subband is calculated.

The threshold calculation is based:-When mammograms are transformed into the CT domain.

The microcalcifications appear :

On each subband Over a very

homogeneous background.

Most of the transform coefficients:-Are grouped around the mean value of

the subband correspond to the background

-The coefficients corresponding to theinjuries are far from background value.

A conservative threshold of 3σi;j is selected:where σi;j is the standard deviation of the corresponding subband y I,j .

Weight Selection

Details….

Exhaustive tests:-Consist on evaluating subjectively a set of 15 different mammograms

-With Different combinations of values,

The weights W1, and W2 are determined:-Selected as W1 = 3 σi;j and W2 = 4 σi;j

These weights are chosen to:keep the relationship W1 < W2:

-Because the W factor is a gain -More gain at the edges are wanted.

A conservative threshold of 3σi;j is selected:where σi;j is the standard deviation of the corresponding subband y I,j .

Metrics

To compare the ability of :

Enhancement achieved by the proposed method.

1. Distribution Separation Measure (DSM),

2. The Target to Background Contrast enhancement (TBC) and

3. The Target to Background Enhancement Measure based on Entropy (TBCE) [14].

Measures used to compare:

14. Sameer S. and Keit B.: An Evaluation on Contrast Enhancement Techniques for Mammographic Breast Masses, IEEETransactions on Information Technology in Biomedicine, vol. 9, (2005) pp. 109-119

Metrics

1. Distribution Separation Measure (DSM) Measures used to compare:

The DSM represents :How separated are the distributions of each mammogram

…………………………(3)DSM = |µucalcE -µtissueE |- |µucalc0 -µtissue0 |

µucalcE = Mean of the microcalcification region of the enhanced imageµucalc0 = Mean of the microcalcification region of the original image

µtissueE = Mean of the surrounding tissue of the enhanced imageµtissue0 = Mean of the surrounding tissue of the enhanced image

Defined by:

Where:

Metrics

2. Target to Background Contrast Enhancement Measure (TBC).

The TBC Quantifies :The improvement in difference between the background and the target(MC).

…………………………(4)

µucalc

µtissue

µucalc

µtissue

µucalc

Defined by:

Where:

Eµucalc

0µucalc

= Standard deviations of the microcalcifications region in the enhanced image

= Standard deviations of the microcalcifications region in the original image

Metrics

3.Target to Background Enhancement Measure Based on Entropy(TBCE)

The TBCE Measures :- An extension of the TBC metric- Based on the entropy of the regions rather

than in the standard deviations

Defined by:

Where:

…………………………(5)

µucalc

µtissue

µucalc

µtissue

µucalc

= Entropy of the microcalcifications region in the enhanced image

= Entropy of the microcalcifications region in the original image

Eµucalc

0µucalc

(a)Original image (b)NSTC method (c)The DWT Method

These regions contain :• Clusters of microcalcifications (target)• surrounding tissue (background).

For visualization purposes :The ROI in the original mammogram are marked with a square.

DMS, TBC and TBCE metrics on the enhanced mammograms

NSCT Method DWT Method

DSM TBC TBCE DSM TBC TBCE

0.853 0.477 0.852 0.153 0.078 0.555

0.818 0.330 0.810 0.094 0.052 0.382

1.000 1.000 1.000 0.210 0.092 0.512

0.905 0.322 0.920 1.000 0.077 1.000

0.936 0.380 0.935 0.038 0.074 0.473

0.948 0.293 0.947 0.469 0.075 0.847

0.665 0.410 0.639 0.369 0.082 0.823

0.740 0.352 0.730 0.340 0.074 0.726

0.944 0.469 0.494 0.479 0.095 0.834

0.931 0.691 0.936 0.479 0.000 0.000

0.693 0.500 0.718 0.258 0.081 0.682

0.916 0.395 0.914 0.796 0.079 0.900

Table 1. Decomposition levels and directions.

Experimental Results Analysis

Mammogram

TBC Matrix

NSCT DWT

The proposed method gives higher results than the wavelet-based method.

Mammogram

TBCE Matrix

NSCT DWT

Mammogram

DSM Matrix

NSCT DWT

Experimental Results AnalysisMesh plot of a ROI containing microcalcifications

(a)The original mammogram

(mdb252.bmp)

(b) The enhanced mammogram

using NSCT

(mdb238.bmp)

using NSCT

(mdb253.bmp)

using NSCT

More peaks corresponding to microcalcifications are enhanced

The background has a less magnitude with respect to the peaks:-The microcalcifications are more visible.

Observation:

Plan of action as follows:

1. Segment the microcalcification(MC) from the enhanced image.

2. Find an attribute based on which I can train the machine

2. Based on feature(size/shape), will move on to classification( benign or malignant)

Reference

1. Alqdah M.; Rahmanramli A. and Mahmud R.: A System of MicrocalcificationsDetection and Evaluation of the Radiologist: Comparative Study of the Three MainRaces in Malaysia, Computers in Biology and Medicine, vol. 35, (2005) pp. 905- 914

2. Strickland R.N. and Hahn H.: Wavelet transforms for detecting microcalci¯cationsin mammograms, IEEE Transactions on Medical Imaging, vol. 15, (1996) pp. 218-229

3. Laine A.F., Schuler S., Fan J., Huda W.: Mammographic feature enhancement bymultiscale analysis, IEEE Transactions on Medical Imaging, 1994, vol. 13, no. 4,(1994) pp. 7250-7260

4. Wang T. C and Karayiannis N. B.: Detection of Microcalci¯cations in Digital Mam-mograms Using Wavelets, IEEE Transaction on Medical Imaging, vol. 17, no. 4,(1989) pp. 498-509

5. Nakayama R., Uchiyama Y., Watanabe R., Katsuragawa S., Namba K. and DoiK.: Computer-Aided Diagnosis Scheme for Histological Classi¯cation of ClusteredMicrocalci¯cations on Magni¯cation Mammograms, Medical Physics, vol. 31, no. 4,(2004) 786 – 799

6. Heinlein P., Drexl J. and Schneider Wilfried: Integrated Wavelets for Enhance-ment of Microcalci¯cations in Digital Mammography, IEEE Transactions on Medi-cal Imaging, Vol. 22, (2003) pp. 402-413

7. Daubechies I.: Ten Lectures on Wavelets, Philadelphia, PA, SIAM, (1992)

8. Zhibo Lu, Tianzi Jiang, Guoen Hu, Xin Wang: Contourlet based mammographicimage enhancement, Proc. of SPIE, vol. 6534, (2007) pp. 65340M-1 - 65340M-8

9. Fatemeh Moayedi, Zohreh Azimifar, Reza Boostani, and Serajodin Katebi:Contourlet-based mammography mass classi¯cation, ICIAR 2007, LNCS 4633,(2007) pp. 923-934

Reference

10. Do M. N. and Vetterli M.: The Contourlet Transform: An efficient DirectionalMultiresolution Image Representation, IEEE Transactions on Image Processing, vol.14, (2001) pp. 2091-2106

11. Da Cunha A. L., Zhou J. and Do M. N,: The Nonsubsampled Contourlet Trans-form: Theory, Design, and Applications, IEEE Transactions on Image Processing,vol. 15, (2006) pp. 3089-3101

12. Burt P. J. and Adelson E. H.: The Laplacian pyramid as a compact image code,IEEE Transactions on Communications, vol. 31, no. 4, (1983) pp. 532-540

13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank forimage analysis and classification, Proceedings of IEEE International Conference onAcoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp. 1417-1420

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Reference

microcalcification enhancement in digital mammogram

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