Optimisation in Signal and Image Processing

by Siarry, Patrick

• ISBN13: 9781848210448
• ISBN10: 1848210442
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-10-12
• Publisher: Wiley-ISTE

Summary

This book describes the optimization methods most commonly encountered in signal and image processing: artificial evolution and Parisian approach; wavelets and fractals; information criteria; training and quadratic programming; Bayesian formalism; probabilistic modeling; Markovian approach; hidden Markov models; and metaheuristics (genetic algorithms, ant colony algorithms, cross-entropy, particle swarm optimization, estimation of distribution algorithms, and artificial immune systems).

Author Biography

Patrick Siarry is Professor of Automatics and Informatics at the University of Paris 12, France.

Table of Contents

Introduction	p. xiii
Modeling and Optimization in Image Analysis	p. 1
Modeling at the source of image analysis and synthesis	p. 1
From image synthesis to analysis	p. 2
Scene geometric modeling and image synthesis	p. 3
Direct model inversion and the Hough transform	p. 4
The deterministic Hough transform	p. 4
Stochastic exploration of parameters: evolutionary Hough	p. 5
Examples of generalization	p. 7
Optimization and physical modeling	p. 9
Photometric modeling	p. 9
Motion modeling	p. 10
Conclusion	p. 12
Acknowledgements	p. 13
Bibliography	p. 13
Artificial Evolution and the Parisian Approach. Applications in the Processing of Signals and Images	p. 15
Introduction	p. 15
The Parisian approach for evolutionary algorithms	p. 15
Applying the Parisian approach to inverse IFS problems	p. 17
Choosing individuals for the evaluation process	p. 18
Retribution of individuals	p. 18
Results obtained on the inverse problems of IFS	p. 20
Conclusion on the usage of the Parisian approach for inverse IFS problems	p. 22
Collective representation: the Parisian approach and the Fly algorithm	p. 23
The principles	p. 23
Results on real images	p. 27
Application to robotics: fly-based robot planning	p. 30
Sensor fusion	p. 34
Artificial evolution and real time	p. 37
Conclusion about the fly algorithm	p. 39
Conclusion	p. 40
Acknowledgements	p. 41
Bibliography	p. 41
Wavelets and Fractals for Signal and Image Analysis	p. 45
Introduction	p. 45
Some general points on fractals	p. 46
Fractals and paradox	p. 46
Fractal sets and self-similarity	p. 47
Fractal dimension	p. 49
Multifractal analysis of signals	p. 54
Regularity	p. 54
Multifractal spectrum	p. 58
Distribution of singularities based on wavelets	p. 60
Qualitative approach	p. 60
A rough guide to the world of wavelet	p. 60
Wavelet Transform Modulus Maxima (WTMM) method	p. 63
Spectrum of singularities and wavelets	p. 66
WTMM and some didactic signals	p. 68
Experiments	p. 70
Fractal analysis of structures in images: applications in microbiology	p. 70
Using WTMM for the classification of textures-application in the field of medical imagery	p. 72
Conclusion	p. 76
Bibliography	p. 76
Information Criteria: Examples of Applications in Signal and Image Processing	p. 79
Introduction and context	p. 79
Overview of the different criteria	p. 81
The case of auto-regressive (AR) models	p. 83
Origin, written form and performance of different criteria on simulated examples	p. 84
AR and the segmentation of images: a first approach	p. 87
Extension to 2D AR and application to the modeling of textures	p. 89
AR and the segmentation of images: second approach using 2D AR	p. 92
Applying the process to unsupervised clustering	p. 95
Law approximation with the help of histograms	p. 98
Theoretical aspects	p. 98
Two applications used for encoding images	p. 99
Other applications	p. 103
Estimation of the order of Markov models	p. 103
Data fusion	p. 104
Conclusion	p. 106
Appendix	p. 106
Kullback (-Leibler) information	p. 106
Nishii's convergence criteria	p. 107
Bibliography	p. 107
Quadratic Programming and Machine Learning-Large Scale Problems and Sparsity	p. 111
Introduction	p. 111
Learning processes and optimization	p. 112
General framework	p. 112
Functional framework	p. 114
Cost and regularization	p. 115
The aims of realistic learning processes	p. 116
From learning methods to quadratic programming	p. 117
Primal and dual forms	p. 117
Methods and resolution	p. 119
Properties to be used: sparsity	p. 120
Tools to be used	p. 120
Structures of resolution algorithms	p. 121
Decomposition methods	p. 121
Solving quadratic problems	p. 123
Online and non-optimized methods	p. 126
Comparisons	p. 127
Experiments	p. 128
Comparison of empirical complexity	p. 128
Very large databases	p. 130
Conclusion	p. 132
Bibliography	p. 133
Probabilistic Modeling of Policies and Application to Optimal Sensor Management	p. 137
Continuum, a path toward oblivion	p. 137
The cross-entropy (CE) method	p. 138
Probability of rare events	p. 139
CE applied to optimization	p. 143
Examples of implementation of CE for surveillance	p. 146
Introducing the problem	p. 147
Optimizing the distribution of resources	p. 149
Allocating sensors to zones	p. 150
Implementation	p. 151
Example of implementation of CE for exploration	p. 153
Definition of the problem	p. 153
Applying the CE	p. 156
Analyzing a simple example	p. 157
Optimal control under partial observation	p. 158
Decision-making in partially observed environments	p. 159
Implementing CE	p. 162
Example	p. 163
Conclusion	p. 166
Bibliography	p. 166
Optimizing Emissions for Tracking and Pursuit of Mobile Targets	p. 169
Introduction	p. 169
Elementary modeling of the problem (deterministic case)	p. 170
Estimability measurement of the problem	p. 170
Framework for computing exterior products	p. 173
Application to the optimization of emissions (deterministic case)	p. 175
The case of a maneuvering target	p. 180
The case of a target with a Markov trajectory	p. 181
Conclusion	p. 189
Appendix: monotonous functional matrices	p. 189
Bibliography	p. 192
Bayesian Inference and Markov Models	p. 195
Introduction and application framework	p. 195
Detection, segmentation and classification	p. 196
General modeling	p. 199
Markov modeling	p. 199
Bayesian inference	p. 200
Segmentation using the causal-in-scale Markov model	p. 201
Segmentation into three classes	p. 203
The classification of objects	p. 206
The classification of seabeds	p. 212
Conclusion and perspectives	p. 214
Bibliography	p. 215
The Use of Hidden Markov Models for Image Recognition: Learning with Artificial Ants, Genetic Algorithms and Particle Swarm Optimization	p. 219
Introduction	p. 219
Hidden Markov models (HMMs)	p. 220
Definition	p. 220
The criteria used in programming hidden Markov models	p. 221
Using mataheuristics to learn HMMs	p. 223
The different types of solution spaces used for the training of HMMs	p. 223
The metaheuristics used for the training of the HMMs	p. 225
Description, parameter setting and evaluation of the six approaches that are used to train HMMs	p. 226
Genetic algorithms	p. 226
The API algorithm	p. 228
Particle swarm optimization	p. 230
A behavioral comparison of the metaheuristics	p. 233
Parameter setting of the algorithms	p. 234
Comparing the algorithms' performances	p. 237
Conclusion	p. 240
Bibliography	p. 240
Biological Metaheuristics for Road Sign Detection	p. 245
Introduction	p. 245
Relationship to existing works	p. 246
Template and deformations	p. 248
Estimation problem	p. 248
A priori energy	p. 248
Image energy	p. 249
Three biological metaheuristics	p. 252
Evolution strategies	p. 252
Clonal selection (CS)	p. 255
Particle swarm optimization	p. 259
Experimental results	p. 259
Preliminaries	p. 259
Evaluation on the CD3 sequence	p. 261
Conclusion	p. 265
Bibliography	p. 266
Metaheuristics for Continuous Variables. The Registration of Retinal Angiogram Images	p. 269
Introduction	p. 269
Metaheuristics for difficult optimization problems	p. 270
Difficult optimization	p. 270
Optimization algorithms	p. 272
Image registration of retinal angiograms	p. 275
Existing methods	p. 275
A possible optimization method for image registration	p. 277
Optimizing the image registration process	p. 279
The objective function	p. 280
The Nelder-Mead algorithm	p. 281
The hybrid continuous interacting ant colony (HCIAC)	p. 283
The continuous hybrid estimation of distribution algorithm	p. 285
Algorithm settings	p. 288
Results	p. 288
Preliminary tests	p. 288
Accuracy	p. 291
Typical cases	p. 291
Additional problems	p. 293
Analysis of the results	p. 295
Conclusion	p. 296
Acknowledgements	p. 296
Bibliography	p. 296
Joint Estimation of the Dynamics and Shape of Physiological Signals through Genetic Algorithms	p. 301
Introduction	p. 301
Brainstem Auditory Evoked Potentials (BAEPs)	p. 302
BAEP generation and their acquisition	p. 303
Processing BAEPs	p. 303
Genetic algorithms	p. 305
BAEP dynamics	p. 307
Validation of the simulated signal approach	p. 313
Validating the approach on real signals	p. 320
Acceleration of the GA's convergence time	p. 321
The non-stationarity of the shape of the BAEPs	p. 324
Conclusion	p. 327
Bibliography	p. 327
Using Interactive Evolutionary Algorithms to Help Fit Cochlear Implants	p. 329
Introduction	p. 329
Finding good parameters for the processor	p. 330
Interacting with the patient	p. 331
Choosing an optimization algorithm	p. 333
Adapting an evolutionary algorithm to the interactive fitting of cochlear implants	p. 335
Population size and the number of children per generation	p. 336
Initialization	p. 336
Parent selection	p. 336
Crossover	p. 337
Mutation	p. 337
Replacement	p. 337
Evaluation	p. 338
Experiments	p. 339
The first experiment with patient A	p. 339
Analyzing the results	p. 343
Second set of experiments: verifying the hypotheses	p. 345
Third set of experiments with other patients	p. 349
Medical issues which were raised during the experiments	p. 350
Algorithmic conclusions for patient A	p. 352
Conclusion	p. 354
Bibliography	p. 354
List of Authors	p. 357
Index	p. 359
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