Nonlinear Digital Filters

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Springer Science & Business Media, Jan 31, 1990 - Technology & Engineering - 392 pages
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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.
 

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the book is very much useful for the researchers who do their work in restoration of images.

Contents

INTRODUCTION
1
12 LINEAR FILTERS
3
13 NONLINEAR FILTERS
4
14 METHODOLOGY
6
STATISTICAL PRELIMINARIES
11
22 INFLUENCE FUNCTION AND MEASURES OF ROBUSTNESS
13
23 MESTIMATORS
18
24 MESTIMATORS OF LOCATION
19
68 MORPHOLOGICAL SKELETONS
188
69 MORPHOLOGICAL SHAPE DECOMPOSITION
198
610 THINNINGS AND THICKENINGS
203
611 GRANULOMETRIES AND THE PECSTRUM
205
612 DISCUSSION
209
HOMOMORPHIC FILTERS
217
72 ALGEBRAIC THEORY OF HOMOMORPHIC SIGNAL PROCESSING
218
73 HOMOMORPHIC FILTERING IN IMAGE ENCHANCEMENT
220

25 MESTIMATORS OF SCALE
22
26 ORDER STATISTICS
24
27 LESTIMATORS
27
28 RESTIMATORS
31
29 DISCUSSION
34
IMAGE FORMATION
37
32 RADIANT SOURCES AND LIGHT REFLECTION
38
33 THE POINTSPREAD FUNCTION OF THE IMAGING SYSTEM
39
34 IMAGE SENSORS AND RECORDERS
40
35 IMAGE SAMPLING AND DIGITIZATION
43
36 MATRIX REPRESENTATION OF DIGITIZED IMAGES
46
37 NOISE IN IMAGE FORMATION
47
38 ELEMENTS OF HUMAN VISUAL PERCEPTION
51
39 IMAGE FORMATION IN THE EYE
53
310 A SYSTEM MODEL FOR HUMAN VISION
55
311 THE IMPLICATIONS OF THE MODEL OF HUMAN VISION TO IMAGE PROCESSING
58
MEDIAN FILTERS
63
43 PROBABILITY DISTRIBUTIONS OF THE MEDIAN FILTERS
65
44 THE MEDIAN AS AN ESTIMATOR OF LOCATION
67
45 MEDIAN FILTERING OF NONWHITE NOISE
73
46 AUTOCORRELATION FUNCTIONS OF THE MEDIAN FILTER OUTPUT
74
47 IMPULSIVE NOISE FILTERING BY MEDIAN FILTERS
76
48 EDGE PRESERVATION PROPERTIES OF THE MEDIAN FILTER
81
49 STREAKING IN MEDIAN FILTERING
85
410 DETERMINISTIC PROPERTIES OF THE MEDIAN FILTER
88
411 SHAPE OF THE ONEDIMENSIONAL ROOT SIGNALS
90
412 SHAPE OF TWODIMENSIONAL ROOT SIGNALS
91
413 CONSTRUCTION OF ROOT SIGNALS
94
414 RATES OF CONVERGENCE OF MEDIAN FILTERS AND APPLICATIONS OF MEDIAN ROOTS
98
415 THRESHOLD DECOMPOSITION OF MEDIAN FILTERS STACK FILTERS
101
416 SEPARABLE TWODIMENSIONAL MEDIAN FILTERS
105
417 RECURSIVE MEDIAN FILTERS
108
418 WEIGHTED MEDIAN FILTERS
111
419 DISCUSSION
112
DIGITAL FILTERS BASED ON ORDER STATISTICS
117
53 MEDIAN HYBRID FILTERS
122
54 RANKEDORDER FILTERS
128
55 TRIMMED MEAN FILTERS
131
56 LFILTERS
135
57 MFILTERS
141
58 RFILTERS
145
59 DISCUSSION
147
MORPHOLOGICAL IMAGE AND SIGNAL PROCESSING
151
62 EROSION AND DILATION IN THE EUCLIDEAN SPACE
158
63 CLOSINGS AND OPENINGS
167
64 GRAYSCALE MORPHOLOGY
170
65 LINKS BETWEEN FUNCTIONS AND SETS
171
66 GRAYSCALE MORPHOLOGICAL TRANSFORMATIONS
175
67 MORPHOLOGICAL FILTERS
181
74 HOMOMORPHIC FILTERING OF SIGNALDEPENDENT NOISE
226
75 NONLINEAR MEAN FILTERS
230
76 HOMOMORPHIC SYSTEMS FOR CONVOLUTION
235
77 PROPERTIES OF THE COMPLEX CEPSTRUM
237
78 REALIZATIONS OF HOMOMORPHIC FILTERS FOR CONVOLUTION
240
79 DISCUSSION
241
POLYNOMIAL FILTERS
245
82 DEFINITION OF POLYNOMIAL FILTERS
246
83 HARMONIC REPRESENTATION AND DESIGN OF QUADRATIC FILTERS
249
84 WIENER FILTERS
251
85 POWER SPECTRUM ANALYSIS
253
86 BISPECTRAL ANALYSIS
255
87 DISCUSSION AND APPLICATIONS
258
ADAPTIVE NONLINEAR FILTERS
267
92 ROBUST ESTIMATORS OF SCALE
268
93 NONLINEAR EDGE DETECTORS
270
94 REJECTION OF IMPULSES BY ORDER STATISTICS
278
95 ADAPTIVE FILTERS BASED ON LOCAL STATISTICS
280
96 DECISION DIRECTED FILTERS
284
97 TWOCOMPONENT IMAGE FILTERING
290
98 ADAPTIVE LFILTERS
295
99 ADAPTIVE VOLTERRA FILTERS
298
910 COMPARISONS OF ADAPTIVE NONLINEAR FILTERS
302
911 DISCUSSION
306
GENERALIZATIONS AND NEW TRENDS
313
102 A GENERAL NONLINEAR FILTER STRUCTURE
314
103 SIGNALDEPENDENT NOISE FILTERING
316
104 COMPUTATIONAL COMPLEXITY OF THE GENERAL NONLINEAR FILTER MODULE
321
105 OVERVIEW OF THE PERFORMANCE OF VARIOUS NONLINEAR FILTERS
325
106 COLOR IMAGE PROCESSING
328
107 ORDERING OF MULTIVARIATE DATA
331
108 MARGINAL ORDER STATISTICS AS ESTIMATORS OF THE MULTIDIMENSIONAL LOCATION
336
109 NEURAL NETWORKS
338
1010 DISCUSSION
340
ALGORITHMS AND ARCHITECTURES
345
113 RUNNING MEDIAN ALGORITHMS
349
114 RUNNING ALGORITHMS FOR SORTING AND MAXMIN SELECTION
355
115 FAST STRUCTURES FOR MEDIAN AND ORDER STATISTICS FILTERING
363
116 MORPHOLOGICAL IMAGE PROCESSORS
366
117 IMPLEMENTATION TECHNIQUES FOR QUADRATIC DIGITAL FILTERS
370
118 MATRIX DESCRIPTION OF QUADRATIC DIGITAL FILTERS
372
119 SYSTOLIC ARRAY IMPLEMENTATION
374
1110 WAVEFRONT ARRAY IMPLEMENTATION
376
1111 MATRIX DESCRIPTION OF 2D FINITESUPPORT QUADRATIC FILTERS
377
1112 REALIZATION OF 2D QUADRATIC FILTERS BASED ON THE LU AND THE LUSV DECOMPOSITIONS
380
1113 DISCUSSION
382
INDEX
389
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About the author (1990)

NIKOS NIKOLAIDIS, PhD, is a senior researcher in the Artificial Intelligence and Information Analysis Laboratory, Department of Informatics, Aristotle University of Thessaloniki, Greece. IOANNIS PITAS, PhD, is a professor in the Department of Informatics, Aristotle University of Thessaloniki, Greece.

Anastasios Venetsanopoulos is a Professor of Electrical and Computer Engineering at Ryerson University in Toronto, Ontario, and a Professor Emeritus with the Edward S. Rogers Department of Electrical and Computer Engineering at the University of Toronto. He has authored eight books, contributed chapters to thirty books and published over 830 technical papers. He is a Fellow of the Engineering Institute of Canada, the IEEE, the Canadian Academy of Engineering and the Royal Society of Canada.