MATHEMATICAL MORPHOLOGY AND ITS APPLICATIONS TO

IMAGE AND SIGNAL PROCESSING

edited by

Petros Maragos Georgia Institute of Technology

Ronald W. Schäfer Georgia Institute of Technology

Muhammad Akmal Butt Georgia Institute of Technology

KLUWER ACADEMIC PUBLISHERS Boston / Dordrecht / London

Contents

Preface xi

Introduction 1

THEORY

Metric Convexity in the Context of Mathematical Morphology P. K. Ghosh and H. J. A. M. Heijmans 7

Support Function and Minkowski Addition of Non-Convex Sets M. Schmitt 15

Lattice Operators Underlying Dynamic Systems J. Mattioli, L. Doyen, and L. Najman 23

Comparison of Multiscale Morphology Approaches: PDE Implemented via Curve Evolution versus Chamfer Distance Transforms

M. A. Butt and P. Maragos 31

An Attribute-Based Approach to Mathematical Morphology E. Breen and R. Jones ' 41

Spatially-Variant Mathematical Morphology: Minimal Basis Representation

M. Charif-Che.fchaouni and D. Schonfeld 49

The Generalized Tailor Problem J. B. T. M. Roerdink 57

Discrete Random Functions: Modeling and Analysis Using Mathematical Morphology

B. Singh and M. U. Siddiqi 65

Morphological Sampling of Random Closed Sets K. Sivakumar and J. Goutsias 73

C O N N E C T I V I T Y

Connectivity on complete lattices J. Scrra 81

Practical Extensions of Connected Operators P. Salembier and A. Oliveras 97

Region Adjacency Graphs and Connected Morphological Operators F. K. Potjer I l l

Space Connectivity and Translation-Invariance J. Crespo 119

FILTERING

Morphological Filters for Dummies H. J. A. M. Heijmans 127

Alternating Sequential Filters by Adaptive-Neighborhood Structuring Functions

U. M. Braga Neto 139

Quadratic Structuring Functions in Mathematical Morphology R. van den Boomgaard, L. Dorst, S. Makram-Ebeid, and J. Schavemaker 147

MRL-Filters and their Adaptive Optimal Design for Image Processing L. Pessoa and P. Maragos 155

Weighted Composite Order-Statistics Filters: Optimal Morphological Pattern Recognition

D. Schonfeld 163

N O N L I N E A R S Y S T E M S R E L A T E D T O M O R P H O L O G Y

Links Between Mathematical Morphology, Rough Sets, Fuzzy Logic and Higher Order Neural Networks

S. Skoneczny, A. Stajniak, J. Szostakowski, and R. Foltyniewicz . . . . 1 7 1

Grey-Scale Soft Morphological Filter Optimization by Genetic Algorithms

N. R. Harvey and S. Marshall 179

Soft Morphological Operators Based on Nonlinear Lp Mean Operators M. Pappas and I. Pitas 187

The Viterbi Optimal Runlength-Constrained Approximation Nonlinear Filter

N. D. Sidiropoulos 195

ALGORITHMS, ARCHITECTURES

Recursive Morphology using Line Structuring Elements D. C. Nadadur and R. M. Haralick 203

A Morphological Algorithm for Linear Segment Detection H. Talbot 219

Toward the Optimal Decomposition of Arbitrarily Shaped Structuring Elements by Means of a Genetic Approach

G. Anelli, A. Broggi, and G. Destri 227

A Data Dependent Architecture Based on Seeded Region Growing Strategy for Advanced Morphological Operators

D. Noguet, A. Merle, D. Lattard 235

Implementing Morphological Image Operators via Trained Neural Networks

С B. Herwig and R. J. Schalkoff 245

GRANULOMETRIES, TEXTURE

Optimal and Adaptive Design of Reconstructive Granulometric Filters E. R. Dougherty and Y. Chen 253

Periodic Lines and Their Application to Granulomctries R. Jones and P. Soille 263

Local Grayscale Granulomeres Based on Opening Trees L. Vincent 273

Integrating Size Information into Intensity Histogram R. A. Lotufo and E. Trettel 281

Probabilistic Model of Rough Surfaces Obtained by Electro-Erosion D. Jeulin and P. Laurenge 289

A Textural Analysis by Mathematical Morphology F. Huet and J. Mattioli 297

S E G M E N T A T I O N

Computation of Watersheds Based on Parallel Graph Algorithms A. Meijster and ./. B. T. M. Roerdink 305

Segmentation Algorithm by Multicriteria Region Merging B. Marcotegui 313

Temporal Stability in Sequence Segmentation using the Watershed Algorithm

F. Marques 321

The Dynamics of Minima and Contours F. Meyer 329

A Morphological Interpolation Method for Mosaic Images F. Meyer 337

I M A G E S E Q U E N C E A N A L Y S I S

Multivalued Morphology and its Application in Moving Object Segmentation and Tracking

С Gu 345

Mathematical Morphology for Image Sequences using the Knowledge of Dynamics

C.-H. Demarty 353

Motion Picture Restoration Using Morphological Tools E. Decenciere Ferrandiere 361

Segmentation-based Morphological Interpolation of Partition Sequences R. Bremond and F. Marques 369

L E A R N I N G , D O C U M E N T A N A L Y S I S

Set Operations on Closed Intervals and their Applications to the Automatic Programming of MMach's

A. J. Barrera, B. G. P. Salas, and C. R. F. Hashimoto 377

Automatic Programming of MMach's for OCR A. J. Barrera, R. Terada, F. S. С da Silva, N. S. Tomita 385

Morphological Preprocessing and Binarization for OCR Systems M. Cumplido, P. Montolio and A. Gasull 393

Adaptive Directional Morphology with Application to Document Analysis

G. Agam and I. Dinstein 401

A P P L I C A T I O N S

Segmentation of 3D Pulmonary Trees Using Mathematical Morphology C. Pisupati, L. Wolff, E. Zerhouni and W. Mitzner 409

Automatic 3-Dimensional Segmentation of MR Brain Tissue using Filters by Reconstruction

./. Madrid and N. Ezquerra 417

Watershed Analysis and Relaxation Labelling: A Cooperative Approach for the Interpretation of Cranial-MR Images Using a Statistical Digital Atlas

/. E. Pratikakis, H. Sahli and J. Cornelis 425

Robust Extraction of Axon Fibers from Large-scale Electron Micrograph Mosaics

R. С Vogt 433

Strong Edge Features for Image Coding J. R. Casas and L. Torres 443

Water Depth Determination using Mathematical Morphology S. M. Lea, M. Lyhanon, and S. H. Peckinpaugh i 451

Geometrical and Topological Characterization of Cork Cells by Digital Image Analysis

P. Pina, N. Selmaoui and M. A. Fortes 459

Author Index 4G7

Subject Index 469