Mathematical Morphology and its Applications to Image and Signal Processing

479 Pages·1996·24.22 MB·English

by  Petros Maragos

MATHEMATICAL MORPHOLOGY
AND ITS APPLICATIONS TO
IMAGE AND SIGNAL PROCESSING
Computational Imaging and Vision
Managing Editor:
MAX A. VIERGEVER
Urecht University, Utrecht, The Netherlands
Editorial Board:
OLIVIER D. FAUGERAS, INRIA, Sophia-Antipolis, France
JAN J. KOENDERlNK, Utrecht University, Utrecht, The Netherlands
STEPHEN M. PIZER, University ofN orth Carolina, Chapel Hill, USA
SABURO TSUn, Osaka University, Osaka, Japan
STEVEN W. ZUCKER, McGill University, Montreal, Canada
MATHEMATICAL MORPHOLOGY
AND ITS APPLICATIONS TO
IMAGE AND SIGNAL PROCESSING
edited by
Petros Maragos
Georgia Institute o/Technology
Ronald W. Schafer
Georgia Institute 0/ Technology
Muhammad Akmal Butt
Georgia Institute o/Technology
KLUWER ACADEMIC PUBLISHERS
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" Library of Congress Cataloging-in-Publication Data
Mathematical morphology and its applications to image and signal
processing 1 edited by Petros Maragos, Ronald W. Schafer, Muhammad
Akmal Butt.
p. cm. --- (Computational imaging and vision)
Includes bibliographical references and indexes.
ISBN-13 :978-1-4613-8063-4 e-ISBN-13 :978-1-4613-0469-2
001: 10 .1 007/978-1-4613-0469-2
I. Image processing--Mathematics. 2. Signal processing--Mathematics.
3. Digital ftlters (Mathematics) 4. Computer vision. I. Maragos, Petros A.,
1957-. II. Schafer, Ronald W., 1938- . III. Butt, Muhammad Akmal.
IV. Series.
TA 1637.M36 1996
006.4'2'OI51--dc20 96-14893
CIP
Copyright @ 1996 by Kluwer Academic Publishers. Second Printing 2001.
Sof'tcover reprint of the hardcover I st edition 1996
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or tr~mitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the publisher,
Kluwer Academic Publishers, WI Philip Drive, Assinippi Park, Norwell,
Massachusetts 02061
Printed on acid-free paper.
This printing is a digital duplication of the original edition.
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. Mamgos ......................................... 31
An Attribute-Based Approach to Mathematical Morphology
E. Breen and R. Jones .............................................. 41
Spatially-Variant Mathematical Morphology: Minimal Basis
Representation
M. Charif-Chefchaouni 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
CONNECTIVITY
Connectivity on complete lattices
J. Serra ............................................................ 81
Practical Extensions of Connected Operators
P. Salembier and A. Oliveras ...................................... 97
Region Adjacency Graphs and Connected Morphological Operators
F. K. Potjer ....................................................... 111
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
NONLINEAR SYSTEMS RELATED TO MORPHOLOGY
Links Between Mathematical Morphology, Rough Sets, Fuzzy Logic
and Higher Order Neural Networks
S. Skoneczny, A. Stajniak, J. Szostakowski, and R. Foltyniewicz .... 171
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. SidiropotUOS ................................................ 195
ALGORITHMS, ARCHITECTURES
Recursive Morphology using Line Structuring Elements
D. C. Nadadur and R. M. Hamlick ................................ 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
C. 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 Granulometries
R. Jones and P. Soille ............................................. 263
Local Grayscale Granulometries Based on Opening Trees
L. Vincent ........................................................ 273
Integrating Size Information into Intensity Histogram
R. A. Lotu/o and E. 7rettel ........................................ 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
SEGMENTATION
Computation of Watersheds Based on Parallel Graph Algorithms
A. Meijster and J. 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
IMAGE SEQUENCE ANALYSIS
Multivalued Morphology and its Application in Moving Object
Segmentation and Thacking
C. 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
LEARNING, DOCUMENT ANALYSIS
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. C. 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 1. Dinstein ......................................... .401
APPLICATIONS
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
J. Madrid and N. Ezquerm ........................................ 417
Watershed Analysis and Relaxation Labelling: A Cooperative
Approach for the Interpretation of Cranial-MR Images
Using a Statistical Digital Atlas
1. E. Pratikakis, H. Sahli and J. Cornelis .......................... 425
Robust Extraction of Axon Fibers from Large-scale Electron
Micrograph Mosaics
R. C. Vogt ........................................................ 433
Strong Edge Features for Image Coding
J. R. Casas and L. TOrTeS ••••••••••••••••••••••••••••••••.•••••••• 443
Water Depth Determination using Mathematical Morphology
S. M. Lea, M. Lybanon, and S. H. Peckinpaugh ........ , ........... 451
Geometrical and Topological Characterization of Cork Cells by
Digital Image Analysis
P. Pina, N. Selmaoui and M. A. Fortes ........................... 459
Author Index ............................................................. 467
Subject Index ............................................................ 469
Preface
The first International Symposium on Mathematical Morphology (ISMM) and its
applications to image and signal processing took place in Barcelona, Spain, in May
1993. The success of this symposium both at the scientific and the organization level
initiated the foundation of the International Society for Mathematical Morphology
which planned a series of international symposia on this subject. Thus, the second
ISMM was held at Fontainebleau, France, in September 1994, and was as successful
and enjoyable as the first ISMM.
The third in this series of symposia is the International Symposium on Math
ematical Morphology and its Applications to Image and Signal Processing held in
Atlanta, Georgia, in May 1996. This edited book consists of the papers presented at
the ISMM'96. The acceptance of these papers among a larger number of submissions
was decided by the Technical Committee and the Local Committee of ISMM'96. The
realization of this book and its prompt preparation so that it can be available to
the attendees of ISMM'96 required coordinated efforts by many people. We wish
to express our thanks to the members of the Technical and Local Committees who
reviewed the submitted papers and to all the authors for providing us with camera
ready manuscripts in time. Special thanks also go to Lucio Pessoa for helping us
with various text processing tasks required for completion of the book. We also
wish to thank the Continuing Education Department of Georgia Tech for helping
us with the overall organization of the symposium and the School of Electrical and
Computer Engineering of Georgia Tech for providing us with technical support and
facilities required to complete this task.
Both the ISMM'93 and ISMM'94 have set a high standard, but we are pleased
with the final papers and hope that the ISMM'96 will be equally stimulating and
enjoyable. As discussed in the Introduction of this book, the papers presented
herein contain interesting research results on the latest theoretical and practical
developments of mathematical morphology and its applications to image analysis.
PETROS MARAGOS
RONALD W. SCHAFER
MUHAMMAD AKMAL BUTT