Table Of ContentFuzzy Techniques in Image Processing
Studies in Fuzziness and Soft Computing
Editor-in-chief
Prof. Janusz Kacprzyk
Systems Research Institute
Polish Academy of Sciences
ul. Newelska 6
01-447 Warsaw, Poland
E-mail: [email protected]
http://www.springer.de/cgi-binlsearch_book.pl?series=2941
Vol. 3. A. Geyer-Schulz Vol. 14. E. Hisdal
Fuzzy Rule-Based Expert Systems and Genetic Ma Logical Structures for Representation
chine Learning, 2nd ed. 1996 of Knowledge and Uncertainty, 1998
ISBN 3-7908-0964-0 ISBN 3-7908-1056-8
Vol. 4. T. Onisawa and J. Kacprzyk (Eds.) Vol. 15. G.J. K1ir and M.J. Wierman
Reliability and Safety Analyses under Uncertainty-Based Information, 2nd ed., 1999
Fuzziness, 1995 ISBN 3-7908-1242-0
ISBN 3-7908-0837-7
Vol. 5. P. Bosc and 1. Kacprzyk (Eds.) Vol. 16. D. Driankov and R. Palm (Eds.)
Advances in Fuzzy Control, 1998
Fuzziness in Database Management
ISBN 3-7908-1090-8
Systems, 1995
ISBN 3-7908-0858-X
Vol. 17. L. Reznik, V. Dimitrov and
Vol. 6. E. S. Lee and Q. Zhu J. Kacprzyk (Eds.)
Fuzzy and Evidence Reasoning, 1995 Fuzzy Systems Design, /998
ISBN 3-7908-0880-6 ISBN 3-7908-1118-1
Vol. 7. B.A. Juliano and W. Bandler Vol. 18. L. Polkowski and A. Skowron (Eds.)
Tracing Chains-of-Thought, 1996 Rough Sets in Knowledge Discovery I, 1998
ISBN 3-7908-0922-5 ISBN 3-7908-11l9-X
Vol. 8. F. Herrera and J. L. Verdegay (Eds.)
Vol. 19. L. Polkowski and A. Skowron (Eds.)
Genetic Algorithms and Soft Computing, 1996
Rough Sets in Knowledge Discovery 2, 1998
ISBN 3-7908-0956-X
ISBN 3-7908-1120-3
Vol. 9. M. Sato et aI.
Fuzzy Clustering Models and Applications, 1997 Vol. 20. J. N. Mordeson and P. S. Nair
ISBN 3-7908-1026-6 Fuzzy Mathematics, 1998
ISBN 3-7908-1121-1
Vol. 10. L. C. Jain (Ed.)
Soft Computing Techniques in Knowledge-based Vol. 21. L. C. Jain and T. Fukuda (Eds.)
Intelligent Engineering Systems, 1997 Soft Computing for Intelligent Robotic Systems,
ISBN 3-7908-1035-5 1998
ISBN 3-7908-1147-5
Vol. II. W. Mielczarski (Ed.)
Fuzzy Logic Techniques in Power Systems, 1998
Vol. 22. J. Cardoso and H. Camargo (Eds.)
ISBN 3-7908-1044-4
Fuzziness in Petri Nets, 1999
Vol. 12. B. Bouchon-Meunier (Ed.) ISBN 3-7908-1158-0
Aggregation and Fusion of Imperfect
1nformation, 1998 Vol. 23. P.S. Szczepaniak (Ed.)
ISBN 3-7908-1048-7 Computational Intelligence and Applications, 1999
ISBN 3-7908-1161-0
Vol. 13. E. Orlowska (Ed.)
Incomplete Information: Vol. 24. E. Orlowska (Ed.)
Rough Set Analysis. 1998 Logic at Work, 1999
ISBN 3-7908-1049-5 ISBN 3-7908-1164-5
continued on page 413
Etienne E. Kerre
Mike Nachtegael (Editors)
Fuzzy Techniques
in Image Processing
With 197 Figures
and 31 Tables
Springer-Verlag Berlin Heidelberg GmbH
Prof. Dr. Etienne E. Kerre
Drs. Mike Nachtegael
Ghent University
Department of Applied Mathematics and Computer Science
Fuzziness and Uncertainty Modelling Research Unit
Krijgslaan 281 (S9)
9000 Gent
Belgium
Email: [email protected]
[email protected]
ISSN 1434-9922
ISBN 978-3-7908-2475-9 ISBN 978-3-7908-1847-5 (eBook)
DOI 10.1007/978-3-7908-1847-5
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Fuzzy techniques in image processing: techniques and applications; with 31 tab les / Etienne E. Kerre; Mike
Nachtegael (ed.). - Heidelberg; New York: Physica-Verl., 2000
(Studies in fuzziness and soft computing; VoI. 52)
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Preface
Since time immemorial, vision in general and images in particular have played
an important and essential role in human life. Nowadays, the field of image
processing also has numerous scientific, commercial, industrial and military
applications. All these applications result from the interaction between fun
damental scientific research on the one hand, and the development of new and
high-standard technology on the other hand. Regarding the scientific com
ponent, quite recently the scientific community became familiar with "fuzzy
techniques" in image processing, which make use of the framework of fuzzy
sets and related theories. The theory of fuzzy sets was initiated in 1965 by
Zadeh, and is one of the most developed models to treat imprecision and
uncertainty. Instead of the classical approach that an object belongs or does
not belong to a set, the concept of a fuzzy set allows a gradual transition
from membership to nonmembership, providing partial degrees of member
ship. Fuzzy techniques are often complementary to existing techniques and
can contribute to the development of better and more robust methods, as
has already been illustrated in numerous scientific branches. With this vol
ume, we want to demonstrate that the introduction and application of fuzzy
techniques can also be very successful in the area of image processing.
This book contains high-quality contributions of over 30 field experts,
covering a wide range of both theoretical and practical applications of fuzzy
techniques in image processing. The chapters have been grouped into three
parts: Fuzzy Mathematical Morphology, Fuzzy Image Filtering and Applica
tions of Fuzzy Techniques in Image Processing.
In the first part we present four chapters on fuzzy mathematical mor
phology. In the first chapter the reader will find an overview of both clas
sical and fuzzy approaches towards mathematical morphology, an extensive
study of their properties, as well as a close look at the links between these
approaches. The second chapter is dedicated to the important property of
(generalized) idempotence. In particular, it is shown under which conditions
this property holds in fuzzy mathematical morphology. Chapter 3 discusses
a specific approach towards fuzzy morphology based on the fuzzification of
the notion of subsethood by using inclusion indicators. Furthermore it ex
plains in which manner binary algorithms lift to fuzzy algorithms, it provides
some basic representation theorems for fuzzy morphological operations, and
VI Preface
it shows how one can define approximate convexity in this context. Finally,
the fourth chapter takes a look at fuzzy morphology and derived spatial rela
tionships such as distance, adjacency and directional relative position. These
spatial relationships are very important and lead to applications in pattern
recognition.
In the second part, five chapters on fuzzy image filtering are presented.
Chapter 5 gives a nice and extensive overview of already existing fuzzy en
hancement and filtering techniques. The following three chapters concern spe
cific (families of) fuzzy rule-based filtering methods: the extended adaptive
weighted fuzzy mean filter is discussed in Chapter 6, Chapter 7 highlights the
merits of the iterative fuzzy control based filter and its modifications, while
Chapter 8 concerns the design of fuzzy rule-based image processing systems
- both for noise removal and edge extraction - by optimizing a nonlinear
function. In every chapter, the performance of the filters is illustrated with
numerous computer simulations. To conclude, Chapter 9 discusses different
kinds of filtering techniques for color images. Among other things, the advan
tages of the RSI color space w.r.t. the RGB color space are considered when
dealing with fuzzy rules in a color environment.
The third part contains six applications of fuzzy techniques in image pro
cessing, including engineering and medical problems. Among them are lin
guistic color processing using fuzzy logic and its application to spot welding,
discussed in Chapter 10. In Chapter 11, fuzzy decision rules are used to
rank segmentation paths before feeding them to a character classifier. In the
third chapter of this part, several fuzzy techniques are considered for the
detection and analysis of potential breast cancer lesions on mammographic
images, yielding very good results. Chapter 13 concerns the design of a fuzzy
motion detector and its successful application to de-interlacing, leading to
highly improved quality of originally interlaced video signals. The problem of
object recognition and visual servoing is treated in Chapter 14. In particu
lar, techniques for recognising partially occluded objects and a fuzzy control
approach for the fine-positioning of a robot gripper using visual data are
presented. Finally, Chapter 15 discusses topology-preserving deformations of
fuzzy pictures.
The editing process was divided in two phases. In the first phase we
reviewed all contributions, focussing our attention on the scientific content
and the readability of the chapters. We hereby are thankful to the authors
for considering our suggestions. In the second phase, we have made many
efforts to produce a consistent and "good-looking" volume. This means for
example that all chapters have the same lay-out details, that all reference
lists have been reproduced in the same style, and that we have tried to make
a good overall index. The index has around 300 entries, and there are a
total of 456 references to specialized scientific literature. Furthermore, the
book contains 188 illustrative figures and diagrams. Note that for technical
reasons, the color figures in chapters 9 and 10 are reproduced in black and
Preface VII
white. However, the original coloured images of these chapters are included
in an appendix at the end of the book.
We are convinced that this volume presents a broad, up-to-date and state
of-the-art coverage of diverse aspects related to fuzzy techniques in image
processing, and illustrates the richness and the enormous potential of these
techniques. As the first of its kind, we hope this book will serve not only as
an important reference for scientists and practitioners in this area, but also
as an inspiration for newcoming researchers.
Gent, Etienne E. K erre
January 2000 Mike Nachtegael
Contents
Preface... .. .... ......... ... ........ ... .... .. .... ........... .. V
Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .I X. . . . . . . . . . . . . .
List of Contributors ......... ... ..... ..... ....... ..... ....... . XV
Part 1. Fuzzy Mathematical Morphology
1. Classical and Fuzzy Approaches towards
Mathematical Morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Mike Nachtegael, Etienne E. Kerre
1 Introduction....... .......... ................................ 3
2 Binary mathematical morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Gray-scale morphology based on the threshold approach . . . . . . .. .. 15
4 Gray-scale morphology based on the umbra approach. . . . . . . . ... . 2. 0
5 Fuzzy mathematical morphology: the general framework . . . . . . ... . 27
6 Fuzzy mathematical morphology: approach of Bloch & Maitre . . .. . 43
7 Fuzzy mathematical morphology: approach of Minkowski addition. . 43
8 Fuzzy mathematical morphology: approach of subset inclusion. . . .. 45
9 Schematic overview of the different approaches towards fuzzy math-
ematical morphology . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . .5 .4 . . . . . . . .
10 Bibliographical remarks. . . . . . . . . . . . . . . . . . . . . . . . . .. .. . 54. . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . 5.6 . . . . . . . . . . . . .
2. Generalized Idempotence in
Fuzzy Mathematical Morphology . . . . . . . . . . . . . . . . . . .. .. . 58. . . . . .
Bernard De Baets
1 Generalized idem potence in binary morphology . . . . . . . . . . . . . 5. 8. . ..
2 Fuzzy morphology: a logical approach ....... .... ... ... .... .. ... 60
3 Residual operators of triangular norms. . . . . . . . . . . . . . . . .. .. .6 .3 . . . .
4 Fuzzy morphology with triangular norms and residual implicators .. 66
5 Idempotent fuzzy closing and fuzzy opening operations ... ........ 67
6 Open and closed fuzzy objects . . . . . . . . . . . . . . . . . . . . . ... . . .6 8 . . . . . .
References ... ....................... ;.. ............. ... ... .. .... 73
X Contents
3. Fuzzy Mathematical Morphology
Based on Fuzzy Inclusion ......... ........... ... ... ..... ..... 76
Edward R. Dougherty, Antony T. Popov
1 Introduction... .... .... .... ... ....... ..... ...... ........ .... . 76
2 Binary mathematical morphology and the abstract lattice theory .. 77
3 Fuzzy morphological operations based on inclusion indicators. . . . .. 81
4 Algorithms.................................................. 88
5 Morphological representation .. ........... ... ........... ..... . 91
6 Indicators of approximate convexity . . . . . . . . . . . . . . . . . . ... . .9 7. . . . .
References .... .......... ...... .... ... ...... ......... .... ....... 98
4. Fuzzy Mathematical Morphology
and Derived Spatial Relationships .... .. .. .... .. ....... .. .. ... 101
Isabelle Bloch
1 Introduction ................................................. 101
2 Definition of basic fuzzy mathematical morphology operators ...... 103
3 Fuzzy distances derived from fuzzy dilation ...................... 113
4 Fuzzy adjacency from fuzzy dilation and set operations ........... 120
5 Fuzzy directional relative position from conditional fuzzy dilation .. 124
6 Concluding remarks ...... .. ...... .......... ...... .... .... .. .. 130
References ... .... ... .. ........ .. .. ... ... ....... ........ ... ... .. 131
Part II. Fuzzy Image Filtering
5. Fuzzy Image Enhancement: An Overview ..... .... .. ..... .. 137
Hamid R. Tizhoosh
1 Introduction ....... ... ...... .. ....... .... .... ... ........... .. 137
2 Framework of fuzzy image processing ........................... 138
3 Fuzzy contrast/brightness adaptation ........................... 140
4 Fuzzy filtering .. ....... ...................... .......... ... .. . 152
5 Subjectivity and image enhancement ........ .............. ..... 162
6 Future view ..... .. ..... ..... .. .. ; .. ........ .. ............ ... 167
References .... ...... ... ...... .. .. ... ..... ... .... .. ...... .... ... 168
6. Adaptive Fuzzy Filter and Its Application
to Image Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 2. . . . . . . . . . .
Chang-Shing Lee, Yau-Hwang Kuo
1 Introduction ........ .... ........... .... .... .... ........ .... .. 172
2 Adaptive weighted fuzzy mean filter ..... .... .... .. ... ... .. .. ... 174
3 Extended AWFM filter for edge enhancement .................... 181
4 Properties of EAWFM filter ................................... 185
5 Experimental results ... ....... ............................... 187
6 Conclusion .................................................. 189
References .. ...... ..... ... ..... .... ......... .. .. ..... ..... ..... 190
Contents XI
7. A Fuzzy Logic Control Based Approach
for Image Filtering ..... ..................... .. ........ .... ... 194
Farzam Farbiz, Mohammad Bagher Menhaj
1 Introduction ................................................. 194
2 The iterative fuzzy control based filter - IFCF ................... 197
3 Smoothing fuzzy control based filter - SFCF ..................... 205
4 The fixed point fuzzy control based filter - FFCF ................ 212
5 Adaptive fixed point fuzzy control based filter - AFCF ............ 213
6 The adaptive C-average fuzzy control based filter - ACFCF ....... 213
7 Conclusion ................... ............ .. ......... ... ..... 219
8 Acknowledgments ...... ...................................... 220
References ..................................................... 220
8. Fuzzy Rule-Based Image Processing with Optimization .... 222
Kaoru Arakawa
1 Introduction ........ .. ........ ............................... 222
2 Principles of fuzzy rule-based image processing ... ............... 223
3 Fuzzy rule-based systems for noise removal ...................... 231
4 Fuzzy rule-based processing for edge extraction .................. 238
5 Concluding remarks .................................. ........ 244
References .... ...... ............ ... ....... ... .................. 246
9. Fuzzy Nonlinear Filtering of Color Images: A Survey ...... 248
Constantin Vertan, Vasile Buzuloiu
1 Introduction ............................... .. ................ 248
2 Crude or pseudo-fuzzy approaches ............................. 251
3 Fuzzy paradigm based filters .. ......................... ... .... 255
4 Fuzzy aggregative filters .................. .... ................ 257
5 Fuzzy inferential filters .................................. ..... 259
6 Conclusions and comments ...... ............. ................. 262
References ................................... .. ........ ........ 262
Part III. Applications of Fuzzy Techniques in Image Processing
10. Fuzzy Color Processing ...................... ............. 267
Lars Hildebrand, Bernd Reusch
1 The human vision system ........................ ............. 267
2 Color models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 6. 8. . . . . . . . . . . .
3 Fuzzy color processing ........................................ 276
4 Example: analysis of welding points ........... ........... ...... 279
5 Summary ................................................... 285
References .......... .. ......................................... 285
