Nonlinear Digital Filters: Principles and Applications

401 Pages·1990·22.034 MB·English

by  I. Pitas, A. N. Venetsanopoulos (auth.)

NONLINEAR DIGITAL FILTERS
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
VLSI, COMPUTER ARCHITECTURE AND
DIGITAL SIGNAL PROCESSING
Consulting Editor
Jonathan Allen
Other books in the series:
Logic Minimization Algorithms for VLSI Synthesis. R.K. Brayton, G.D. Hachtel, C.T. McMullen, and
Alberto Sanngiovanni-Vincentelli. ISBN 0-89838-164-9.
Adaptive Filters: Structures, Algorithms, and Applications. M.L. Honig and D.O. Messerschmitt.
ISBN 0-89838-163-0.
Introduction to VLSI Silicon Devices: Physics, Technology and Characterization. B. El-Kareh and
R.J. Bombard. ISBN 0-89838-210-6.
Latchup in CMOS Technology: The Problem and Its Cure. R.R. Troutman. ISBN 0-89838-215-7.
Digital CMOS Circuit Design. M. Annaratone. ISBN 0-89838-224-6.
The Bounding Approach to VLSI Circuit Simulation. C.A. Zukowski. ISBN 0-89838-176-2.
Multi-Level Simulation for VLSI Design. D.D. Hill and D.R. Coelho. ISBN 0-89838-184-3.
Relaxation Techniques for the Simulation of VLSI Circuits. J. White and A. Sangiovanni-Vincentelli.
ISBN 0-89838-186-X.
VLSI CAD Tools and Applications. W. Fichtner and M. Morf, Editors. ISBN 0-89838-193-2.
A VLSI Architecture for Concurrent Data Structures. W.J. Dally. ISBN 0-89838-235-1.
Yield Simulation for Integrated Circuits. D.M.H. Walker. ISBN 0-89838-244-0.
VLSI Specification, Verification and Synthesis. G. Birtwistle and P.A. Subrahmanyam.
ISBN 0-89838-246-7.
Fundamentals of Computer-Aided Circuit Simulation. W.J. McCalla. ISBN 0-89838-248-3.
Serial Data Computation. S.G. Smith, P.B. Denyer. ISBN 0-89838-253-X.
Phonologic Parsing in Speech Recognition. K.W. Church. ISBN 0-89838-250-5.
Simulated Annealing for VLSI Design. D.F. Wong, H.W. Leong, C.L. Liu. ISBN 0-89838-256-4.
Polycrystalline Silicon for Integrated Circuit Applications. T. Kamins. ISBN 0-89838-259-9.
FET Modeling for Circuit Simulation. D. Divekar. ISBN 0-89838-264-5.
VLSI Placement and Global Routing Using Simulated Annealing. C. Sechen. ISBN 0-89838-281-5.
Adaptive Filters and Equalizers. B. Mulgrew, C.F.N. Cowan. ISBN 0-89838-285-8.
Computer-Aided Design and VLSI Device Development, Second Edition. K.M. Cham, S-Y. Oh, J.L. Moll,
K. Lee, P. VandeVoorde, D. Chin. ISBN: 0-89838-277-7.
Automatic Speech Recognition. K-F. Lee. ISBN 0-89838-296-3.
Speech Time-Frequency Representations. M.D. Riley. ISBN 0-89838-298-X.
A Systolic Array Optimizing Compiler. M.S. Lam. ISBN: 0-89838-300-5.
Algorithms and Techniques for VLSI Layout Synthesis. D. Hill, D. Shugard, J. Fishburn, K. Keutzer.
ISBN: 0-89838-301-3.
Switch-Level Timing Simulation of MOS VLSI Circuits. V.B. Rao, D.V. Overhauser, T.N. Trick,
I. N. Hajj. ISBN 0-89838-302-1.
VLSI for Artificial Intelligence. J.G. Delgado-Frias, W.R. Moore (Editors). ISBN 0-7923-9000-8.
Wafer Level Integrated Systems: Implementation Issues. S.K. Tewksbury. ISBN 0-7923-9006-7.
The Annealing Algorithm. R.H.J.M. Otten & L.P.P.P. van Ginneken. ISBN 0-7923-9022-9.
VHDL: Hardware Description and Design. R. Lipsett, C. Schaefer and C. Ussery. ISBN 0-7923-9030-X.
The VHDL Handbook. D. Coelho. ISBN 0-7923-9031-8.
Unified Methods for VLSI Simulation and Test Generation. K.T. Cheng and V.D. Agrawal.
ISBN 0-7923-9025-3.
ASIC System Design with VHDL: A Paradigm. S.S. Leung and M.A. Shan blatt. ISBN 0-7923-9032-6.
BiCMOS Technology and Applications. A.R. Alvarez (Editor). ISBN 0-7923-9033-4.
Analog VLSIImp!ementation of Neural Systems. C. Mead and M. Ismail (Editors). ISBN 0-7923-9040-7.
The MIPS-X RISC Microprocessor. P. Chow. ISBN 0-7923-9045-8.
Nonlinear Digital Filters: Principles and Applications. I. Pitas and A.N. Venetsanopoulos.
ISBN 0-7923-9049-0.
Algorithmic and Register-Transfer Level Synthesis: The System Architect's Workbench. D.E. Thomas,
E.D. Lagnese, R.A. Walker, J.A. Nestor, J.V. Rajan, R.L. Blackburn. ISBN 0-7923-9053-9.
VLSI Design for Manufacturing: Yield Enhancement. S.W. Director, W. Maly, A.J. Strojwas.
ISBN 0-7923-9053-7.
NONLINEAR DIGITAL FILTERS
PRINCIPLES AND APPLICATIONS
by
I. Pitas
Aristotelian University of Thessaloniki, Greece
and
A.N. Venetsanopoulos
University of Toronto, Canada
'~·'
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Pitas, 1. (Ioannis)
Nonliner digital filters : principles and applications / by
1. Pitas and A.N. Venetsanopoulos.
p. cm. - (The Kluwer international series in engineering and
computer science. VLSI, computer architecture and digital signal
processing)
Inc1udes bibliographical references.
ISBN 978-1-4419-5120-5 ISBN 978-1-4757-6017-0 (eBook)
DOI 10.1007/978-1-4757-6017-0
1. Electric filters, Digital. 1. Venetsanopoulos, A. N.
(Anastasios N.), 1941- II. Title. III. Series.
TK7872.F5P58 1990
621.3815 '324-dc20 89-26769
CIP
Copyright © 1990 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1990
Fourih Printing 1999.
AII rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC.
TABLE OF CONTENTS
Preface ix
List of symbols xi
1. Introduction
1.1 Overview 1
1.2 Linear filters 3
1.3 Nonlinear filters 4
1.4 Methodology 6
2. Statistical preliminaries
2.1 Introduction 11
2.2 Influence function and measures of robustness 13
2.3 M -estimators 18
2.4 M-estimators of location 19
2.5 M-estimators of scale 22
2.6 Order statistics 24
2.7 L-estimators 27
2.8 R-estimators 31
2.9 Discussion 34
3. Image formation
3.1 Introduction 37
3.2 Radiant sources and light reflection 38
3.3 The point-spread function of the imaging system 39
3.4 Image sensors and recorders 40
3.5 Image sampling and digitization 43
3.6 Matrix representation of digitized images 46
3.7 Noise in image formation 47
3.8 Elements of human visual perception 51
3.9 Image formation in the eye 53
3.10 A system model for human vision 55
3.11 The implication of the model of human vision
to image processing 58
4. Median filters
4.1 Introduction 63
4.2 Definition of the median filter 63
4.3 Probability distributions of the median filters 65
4.4 The median as an estimator of location 67
4.5 Median filtering of nonwhite noise 73
vi
4.6 Autocorrelation functions of the median filter output 74
4.7 Impulsive noise filtering by median filters 76
4.8 Edge preservation properties of the median filter 81
4.9 Streaking in median filtering 85
4.10 Deterministic properties of the median filter 88
4.11 Shape of the one-dimensional root signals 90
4.12 Shape of the two-dimensional root signals 91
4.13 Construction of root signals 94
4.14 Rates of convergence of median filters and
applications of median roots 98
4.15 Threshold decomposition of median filters. Stack filters 101
4.16 Separable two-dimensional median filters 105
4.17 Recursive median filters 108
4.18 Weighted median filters 111
4.19 Discussion 112
5. Digital filters based on order statistics
5.1 Introduction 117
5.2 Max/median filters and multistage median filters 117
5.3 Median hybrid filters 122
5.4 Ranked-order filters 128
5.5 Trimmed mean filters 131
5.6 L-filters 135
5.7 M-filters 141
5.8 R-filters 145
5.9 Discussion 147
6. Morphological image and signal processing
6.1 The principles of mathematical morphology 151
6.2 Erosion and dilation in the Euclidean space 158
6.3 Closings and openings 167
6.4 Grayscale morphology 170
6.5 Links between functions and sets 171
6.6 Grayscale morphological transformations 175
6.7 Morphological filters 181
6.8 Morphological skeletons 188
6.9 Morphological shape decomposition 198
6.10 Thinnings and thickenings 203
6.11 Granulometries and the pecstrum 205
6.12 Discussion 209
vii
7. Homomorphic filters
7.1 Introduction 217
7.2 Algebraic theory of homomorphic signal processing 218
7.3 Homomorphic filtering in image enhancement 220
7.4 Homomorphic filtering of signal-dependent noise 226
7.5 Nonlinear mean filters 230
7.6 Homomorphic systems for convolution 235
7.7 Properties of the complex cepstrum 237
7.8 Realizations of homomorphic filters for convolution 240
7.9 Discussion 241
8. Polynomial filters
8.1 Introduction 245
8.2 Definition of polynomial filters 246
8.3 Harmonic representation and design of quadratic filters 249
8.4 Wiener filters 251
8.5 Power spectrum analysis 253
8.6 Bispectral analysis 255
8.7 Discussion and applications 258
9. Adaptive nonlinear filters
9.1 Introduction 267
9.2 Robust estimators of scale 268
9.3 Nonlinear edge detectors 270
9.4 Rejection of impulses by order statistics 278
9.5 Adaptive filters based on local statistics 280
9.6 Decision directed filters 284
9.7 Two-component image filtering 290
9.8 Adaptive £-filters 295
9.9 Adaptive Volterra filters 298
9.10 Comparisons of adaptive nonlinear filters 302
9.11 Discussion 306
10. Generalizations and new trends
10.1 Introduction 313
10.2 A general nonlinear filter structure 314
10.3 Signal-dependent noise filtering 316
10.4 Computational complexity of the
general nonlinear filter module 321
10.5 Overview of the performance of various nonlinear filters 325
10.6 Color image processing 328
10.7 Ordering of multivariate data 331
viii
10.8 Marginal order statistics as estimators of the
multidimensional location 336
10.9 Neural networks 338
10.10 Discussion 340
11. Algorithms and architectures
11.1 Introduction 345
11.2 Sorting and selection algorithms 345
11.3 Running median algorithms 349
11.4 Running algorithms for sorting and max/min selection 355
11.5 Fast structures for median and order statistics filtering 363
11.6 Morphological image processors 366
11.7 Implementation techniques for quadratic digital filters 370
11.8 Matrix description of quadratic digital filters 372
11.9 Systolic array implementation 374
11.10 Wavefront array implementation 376
11.11 Matrix description of 2-d finite-support quadratic filters 377
11.12 Realization of 2-d quadratic filters based on the LU and the
LU-SV decompositions 380
11.13 Discussion 382
Index 389
PREFACE
The function of a filter is to transform a signal into another one more suit
able for a given purpose. As such, filters find applications in telecommunica
tions, radar, sonar, remote sensing, geophysical signal processing, image pro
cessing, and computer vision. Numerous authors have considered deterministic
and statistical approaches for the study of passive, active, digital, multidimen
sional, and adaptive filters. Most of the filters considered were linear although
the theory of nonlinear filters is developing rapidly, as it is evident by the
numerous research papers and a few specialized monographs now available.
Our research interests in this area created opportunity for cooperation and co
authored publications during the past few years in many nonlinear filter families
described in this book. As a result of this cooperation and a visit from John
Pitas on a research leave at the University of Toronto in September 1988, the
idea for this book was first conceived. The difficulty in writing such a mono
graph was that the area seemed fragmented and no general theory was available
to encompass the many different kinds of filters presented in the literature.
However, the similarities of some families of nonlinear filters and the need for
such a monograph providing a broad overview of the whole area made the pro
ject worthwhile. The result is the book now in your hands, typeset at the
Department of Electrical Engineering of the University of Toronto during the
summer of 1989.
The purpose of this book is to fill an existing gap in the scientific litera
ture. It presents the state of the art in the area of nonlinear filters. It is broad
enough to cover various families of nonlinear filters. It is written at a level
which can be easily understood by a graduate student in Electrical Engineering
or Computer Science. Therefore, it can be used as a textbook, that covers part
of a modem graduate digital signal processing course. It can also be used as a
textbook for a graduate course on nonlinear digital signal processing. It con
tains analysis, design algorithms, and digital signal processor architectures for
nonlinear filtering. Thus it is useful to a research or development engineer.
Furthermore, since it offers an up-to-date survey of the relevant research, it can
be used as a reference text by researchers.
The book can be read in many different ways, other than in the order in
which it was written. Readers interested in order statistic or median filters may
be interested in reading it in the following order: chapters 1, 2, 3, 4, 5, 9, 10,
and 11. Others with an interest in morphological filters may choose the order:
X
chapters 1, 3, 6, and 11. Homomorphic filters can be studied by reading the
book as follows: chapters 1, 3, 7. Polynomial (Volterra) type filters can be stu
died by following chapters 1, 3, 8, 9, and then going to chapter 11.
We are grateful to the following reviewers for their informative inputs and
highly valuable suggestions: Prof. M. Omair Ahmad of Concordia University,
Prof. Gonzalo Arce of the University of Delaware, Prof. Saleem Kassam of the
University of Pennsylvania, Prof. Petros Maragos of Harvard University, and
Prof. Giovanni Siccuranza of the University of Trieste, Italy. We would also
like to thank our students AL-Shebeily Saleh, Kostas Kotropoulos, Renee Mar
tens, Sunil Sanwalka, and Ziheng Zhou for reading various chapters of the
manuscript and contributing to the example and figures of the book, Dr. George
Lampropoulos for proofreading the manuscript and Linda Espeut for contribut
ing to the typing of the manuscript.