Fuzzy algorithms: with applications to image processing and pattern recognition (Advances in fuzzy systems, v. 10)

238 Pages·1996·18.84 MB·English

by  Zheru Chi

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ADVANCES IN FUZZY SYSTEMS APPLICATIONS AND THEORY
Honorary Editor: Lotfi A. Zadeh (Univ. of California, Berkeley)
Series Editors: Kaoru Hirota (Tokyo lnst. of Tech.),
George J. Klir (Binghamton U n i-~S UNY),
Elie Sanchez (Neurinfo),
Pei-Zhuang Wang (West Texas A&M Univ.),
Ronald R. Yager (lona College)
Vol. 1: Between Mind and Computer: Fuzzy Science and Engineering
(Eds. P.-Z. Wang and K.-F. Loe)
Vol. 2: Industrial Applications of Fuzzy Technology in the World
(Eds. K. Hirota and M. Sugeno)
Vol. 3: Comparative Approaches to Medical Reasoning
(Eds. M. E. Cohen and D. L. Hudson)
Vol. 4: Fuuy Logic and Soft Computing
(Eds. B. Bouchon-Meunier, R. R. Yager and L. A. Zadeh)
Vol. 5: Fuzzy Sets, Fuzzy Logic, Applications
( G. Bojadziev and M. Bojadziev)
Vol. 6: Fuuy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers
by Lotfi A. Zadeh
(Eds. G. J. Klir and B. Yuan)
Vol. 8: Foundations and Applications of Possibility Theory
(Eds. G. de Cooman, D. Ruan and E. E. Kerre)
Vol. 10: Fuzzy Algorithms: With Applications to Image Processing and
Pattern Recognition
(Z. Chi, H. Yan and T. D. Pham)
Forthcoming volumes:
Vol. 7: Genetic Algorithms and Fuzzy Logic Systems: Soft Computing
Perspectives
(Eds. E. Sanchez, T. Shibata and L. A. Zadeh)
Vol. 9: Fuzzy Topology
(Y. M. Liu and M. K Luo)
Vol. 11 : Hybrid Intelligent Engineering Systems
(Eds. L. C. Jain and R. K. Jain)
Vol. 12: Fuzzy Logic for Business, Finance, and Management
(G. Bojadziev and M. Bojadziev)
Vol. 13: Fuzzy and Uncertain Object-Oriented Databases: Concepts and Models
(Ed. R. de Caluwe)

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Advances in Fuzzy Systems Applications and Theory Vol. 10
FUZZY ALGORITHMS:
With Applications to
Image Processing and Pattern Recognition
Zheru Chi
Hong Kong Polytechnic Universik Hong Kong
Hong Yan
University of Sydney, Australia
Tuan Pham
University of Sydney, Australia
World Scientific
Singapore @NewJ erseyeL. ondon Hong Kong
l
Published by
World Scientific Publishing Co. Re. Ltd.
P 0 Box 128, Farrer Road, Singapore 9 12805
USA ofice: Suite lB, 1060 Main Street, River Edge, NJ 07661
UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Chi, Zheru.
Fuzzy algorithms : with applications to image processing and
pattern recognition I Zheru Chi, Hong Yan, Tuan Pharn.
p. cm.
Includes bibliographical references and index.
ISBN 9810226977
1. Image processing -- Digital techniques. 2. Pattern recognition
systems. 3. Fuzzy algorithms. I. Yan, Hong. 11. Pham, Tuan.
111. Title.
TA1637.C48 1996
006.4'2'0151 13--dc20 96-3 1969
CIP
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright O 1996 by World Scientific Publishing Co. Re. Ltd.
All rights reserved. This book, or parts thereoj may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
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For photocopying of material in this volume, please pay a copying fee through the Copyright
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This book is printed on acid-free paper.
Printed in Singapore by Uto-Print
Preface
In the fields of image processing and pattern recognition, a great number of differ-
ent techniques have been investigated, developed, and implemented in the last few
decades. Starting from statistical models to neural network algorithms, researchers
from all over the world have made a good number of contributions to the development
of improved methodologies for solving difficult problems in these fields.
Sine L. A. Zadeh introduced the fuzzy set theory in 1965, the fuzzy system ap-
proach has been an increasing interest of many scientists and engineers for opening up
a new area of research and problem solving. Many books on fuzzy systems have since
been published. However, most of them are devoted to the theoretical developments
and their applications in control systems. In the last few years, we have also seen the
booming of applications of fuzzy algorithms in image processing and pattern recog-
nition. The interest in using fuzzy algorithms comes from the facts that: (1) fuzzy
rules are found to be naturally effective for any human-like cognition systems such
as image understanding and pattern recognition, and (2) the theory of fuzzy sets
provides a good platform for dealing with noisy, and imprecise information which is
often encountered in our daily life.
This book does not focus on the theoretical research of fuzzy algorithms, but it
rather provides a comprehensive discussion on several issues of application-oriented
methodologies using fuzzy algorithms for image processing and pattern recognition.
These include the segmentation of a variety of images and characterization of tissues
in magnetic resonance (MR) images, parameter identification for mining deposits,
and printing and handwritten character recognition.
This book is mainly aimed at three groups of readers, (1) those who are famil-
iar with fuzzy algorithms and want to identify the useful applications of fuzzy logic,
(2) those who have been articulating in the fields of image processing and pattern
recognition for some years and want to find some new and interesting topics to work
on, and (3) those who want to know more about both fuzzy algorithms and their prac-
tical applications. As an application-oriented book, university students, researchers,
and engineers would find the book useful in many practical aspects. In addition, this
book can serve as supplementary reading material for university courses in areas of
image processing, pattern recognition, artificial intelligence, and fuzzy systems.
This book is divided into seven chapters. Following an introductory chapter is the
generation of membership functions from training examples. Then each of the remain-
ing chapters is devoted to a specific fuzzy algorithm or a class of fuzzy algorithms,
and their applications in image processing and pattern recognition.
In Chapter 1 we introduce the basic concepts and ideas of fuzzy set theory,
including probability and fuzziness, basic properties, some operations on fuzzy sets,
and fuzzy relations. The chapter ends with a brief discussion on fuzzy models for
image processing and pattern recognition.
In Chapter 2 three clustering-based techniques (c-means, adaptive vector quan-
tization, and the self-organizing map) for membership function generation will be
presented. Two techniques for tuning membership functions using the gradient de-
scent algorithm and a neural network approach are also discussed.
In Chapter 3 we discuss Huang and Wang's fuzzy thresholding algorithm follow-
ing the introduction of the threshold selection method based on stati stical decision
theory and non-fuzzy thresholding algorithms. A unified description of all fuzzy or
non-fuzzy thresholding methods is then given and the extension of the methods to
multilevel thresholding is proposed. Finally, the applications of these thresholding
methods to real images are provided.
In Chapter 4 we describe and compare the hard and fuzzy c-mearrs algorithms,
which can be used for clustering when the number of clusters is known. We then
describe three cluster validity measures which can be used to analyze the quality of
fuzzy clustering procedures. The chapter ends with a section on applying the fuzzy
clustering algorithms to several real world image processing and pattern recognition
problems.
In Chapter 5 we first describe how to use membership functions to measure sim-
ilarities between line segments. A basic algorithm for line pattern matching based on
spatial relations of the lines in a prototype and the input pattern is discussed. We
then propose more sophisticated algorithms to deal with noisy patterns and geomet-
rically distorted patterns. To demonstrate the usefulness of the proposed line pattern
matching algorithms, applications to Chinese character recognit ion and point pat tern
matching are illustrated.
In Chapter 6 we present three fuzzy rule generation techniques based on learning
from examples: Wang and Mendel's method, ID3 decision rules, and Krishnapuram's
neural network approach. We then describe the minimization of fuzzy rules based on
Karnaugh maps proposed by Hung and Fernandez and discuss various defuzzification
methods for fuzzy rule-based recognition systems. The chapter ends with a section
on applications of fuzzy rule recognition systems for segmentation of geographic map
images and recognition of printed upper-case English letters and handwritten digits.
In Chapter 7 we introduce several multi-classifier combination techniques for
improving classification performance including voting schemes, a maximum posteriori
probability based method, a multilayer perceptron approach, and a fuzzy integral
model. The chapter ends with a section on applying these combination classifiers to
handwritten numeral character recognition.
Acknowledgements
Much of our work described in this book was funded by the Australian Research Coun-
cil (ARC), the Australian Department of Industry, Science and Technology (DIST),
the Japanese Ministry of Industry and International Trade (MITI) and the Real World
Computing Partnership (RWCP). We would like to thank these funding bodies for
their support.
Some work reported in the book was done by our colleagues, Ms. Jing Wu and
Dr. Mark Suters. We would like to express our sincere appreciation for their contri-
bution. We are also deeply grateful to our publisher, World Scientific Publishing Co.,
for their helpful suggestions in the production of this book.
Finally, we would like to offer our deepest and most heartfelt thanks to our wives
and children for their support, encouragement and patience.

Contents
Preface
1 Introduction
. . . . . . . . . . . . . . . . . . . . . .
1.1 Basic Concepts of Fuzzy Sets
. . . . . . . . . . . . . . . . . . . .
1.1.1 Probability and Fuzziness
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Fuzzy Sets
. . . . . . . . . . . . . . . . . . . . .
1.1.3 Properties of Fuzzy Sets
. . . . . . . . . . . . . . . . . . . .
1.1.4 Operations on Fuzzy Sets
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Fuzzy Relations
1.3 Fuzzy Models for Image Processing and Pattern Recognition . . . . .
2 Membership Functions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Introduction
2.2 Heuristic Selections . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Clustering Approaches
. . . . . . . . . . . . . . . . . .
2.3.1 C-means Clustering Approach
. . . . . . . . . .
2.3.2 Learning with Adaptive Vector Quantization
2.3.3 Self-organizing Map Approach . . . . . . . . . . . . . . . . . .
. . . . . . . . . .
2.3.4 Merging Neighboring Membership Functions
. . . . . . . . . . . . . . . . . . . .
2.4 Tuning of Membership Functions
. . . . . . . . . . . . . . . . . . .
2.4.1 Gradient Descent Algorithm
. . . . . . . . . . . . . . . . . . . .
2.4.2 Neural Network Approach
. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Concluding Remarks
3 Optimal Image Thresholding
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Introduction
3.2 Threshold Selection Based on Statistical Decision Theory . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
3.2.1 Statistical Decision Rule
. . . . . . . . . . . . . . . . . . . . . .
3.2.2 Gaussian Distributions
3.3 Non-fuzzy Thresholding Algorithms . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
3.3.1 Model Fitting Method
. . . . . . . . . . . . . . . . . . .
3.3.2 Otsu's Thresholding Method
. . . . . . . . . . . . .
3.3.3 Minimum Error Thresholding Method