Fuzzy 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) This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is pennilled only under the provisions of the German Copyright Law of September 9, 1965, in its current version, Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000 Originally published by Physica-Verlag Heidelberg in 2000 Softcover reprint of the hardcover 1s t edition 2000 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Hardcover Design: Erich Kirchner, Heidelberg 88/2202-5 4 3 2 1 O - Printed on acid-free paper 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