Statistical Image Processing Techniques for Noisy Images: An Application-Oriented Approach

by Phillipe Rïfrïgier, Franïois Goudail

Overview

Statistical Processing Techniques for Noisy Images presents a statistical framework to design algorithms for target detection, tracking, segmentation and classification (identification). Its main goal is to provide the reader with efficient tools for developing algorithms that solve his/her own image processing applications. In particular, such topics as hypothesis test-based detection, fast active contour segmentation and algorithm design for non-conventional imaging systems are comprehensively treated, from theoretical foundations to practical implementations. With a large number of illustrations and practical examples, this book serves as an excellent textbook or reference book for senior or graduate level courses on statistical signal/image processing, as well as a reference for researchers in related fields.

Product Details

ISBN-13:	9781461346920
Publisher:	Springer US
Publication date:	11/17/2013
Edition description:	2004
Pages:	254
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

	Preface	xi
1.	Introduction	1
1.1	General introduction	1
1.2	Image processing tasks	2
1.3	Statistical decision and estimation theory	4
1.4	An application-oriented approach	5
1.5	Outline of the book	6
2.	Linear Filters: Heuristic Theory and Stability	9
2.1	The different approaches to filter design	10
2.2	Heuristic criteria and optimal filters	11
2.2.1	Noise robustness characterization and matched filter	12
2.2.2	Sharpness of the correlation peak and inverse filter	15
2.2.3	Optical efficiency and phase-only filter	16
2.2.4	Discrimination capability	19
2.2.5	Optimal SDF filters	20
2.2.6	Optimal Trade-off filters	22
2.2.7	Optimal Trade-off SDF filters	23
2.3	Analysis of the stability of linear filters	26
2.4	Regularization of filters	28
2.4.1	Truncature method for regularization	29
2.4.2	Stabilizing functional	29
2.4.3	Some processing examples with stabilized filters	34
2.5	An example of application: Angle estimation of two-dimensional objects	38
2.6	Conclusion	41
2.A	Appendix--Definitions and notation	42
2.B	Appendix--Lagrange multipliers	46
3.	Statistical Correlation Techniques	49
3.1	Some sources of noise in images	50
3.1.1	Nonoverlapping noise	50
3.1.2	Fluctuations of the target's gray levels	52
3.1.3	Additive noise with unknown PSD	52
3.2	Background on statistical decision and estimation theory	53
3.2.1	Decision and estimation theory without nuisance parameters	53
3.2.2	Decision and estimation theory in presence of nuisance parameters	58
3.2.3	Two-hypothesis testing	60
3.3	Matched filtering and statistical decision theory	63
3.4	Optimal filter for unknown PSD	66
3.4.1	ML estimation of the spectral density	67
3.4.2	MAP estimation of the spectral density	69
3.4.3	Marginal Bayesian approach	71
3.4.4	Examples of application	72
3.5	Target location in nonoverlapping noise	74
3.5.1	The SIR image model and optimal location algorithms	74
3.5.2	Targets with known graylevels	77
3.5.3	Targets with fluctuating graylevels	79
3.5.4	Partially fluctuating targets	81
3.6	Conclusion	85
3.A	Appendix--MAP location algorithm in the presence of uniform prior	86
4.	Applications of Statistical Correlation Techniques to Different Physical Noises	89
4.1	A general framework for designing image processing algorithms	90
4.1.1	Generalization of the SIR image model	90
4.1.2	The exponential family	94
4.2	Performing object location with algorithms based on the SIR image model	98
4.2.1	The whitening process	101
4.2.2	The generalized likelihood ratio test (GLRT) approach	104
4.2.3	The implementation issue	108
4.3	Application to binary images: Comparison of optimal and linear techniques	108
4.3.1	The GLRT algorithm for binary images	109
4.3.2	A linear approximation to the GLRT algorithm	111
4.4	Application to edge extraction in SAR images	113
4.4.1	GLRT adapted to speckled images	114
4.4.2	Bias on edge location	118
4.5	Conclusion	122
4.A	Appendix--Basics of estimation theory	123
5.	Statistical Snake-based Segmentation Adapted to Different Physical Noises	129
5.1	Active contours	130
5.1.1	Snake energy	130
5.1.2	The limits of the classical snake	133
5.1.3	Geodesic snakes	133
5.1.4	The level set implementation of snakes	134
5.1.5	Region-based approaches	134
5.2	The SIR Active Contour and its fast implementation	137
5.2.1	Solution for exponential family laws	138
5.2.2	Implementation of a fast statistic calculation	140
5.3	Application to polygonal active contour	146
5.3.1	Regularization of the contour	147
5.3.2	Minimization procedure	148
5.3.3	Discussion	150
5.3.4	Some examples of application	152
5.4	Applications to tracking in video sequences	155
5.4.1	Fixed camera	156
5.4.2	Moving camera	160
5.5	Application to accuracy improvement of edge location	163
5.A	Appendix--Crossing tests	167
6.	Some Developments of the Polygonal Statistical Snake and Their Applications	169
6.1	Generalization of the statistical snake to multichannel images	170
6.2	MDL-based statistical snake	172
6.2.1	The MDL principle	172
6.2.2	Application of the MDL principle to the polygonal statistical snake	174
6.2.3	Two-step optimization process	176
6.2.4	Results obtained with different types of noises	179
6.2.5	Quantitative evaluation of the segmentation performance	183
6.3	Statistical active grid and application to SAR image segmentation	188
6.3.1	Statistical active grid	189
6.3.2	Implementation issues	190
6.3.3	Some segmentation examples	192
6.3.4	Conclusion	193
7.	An Example of Application: Processing of Coherent Polarimetric Images	197
7.1	Basics of polarimetric imaging	197
7.1.1	The representation of polarized light	199
7.1.2	Active polarimetric imaging systems	201
7.1.3	Model of coherent polarimetric images	202
7.2	Processing degree of polarization (DOP) images	203
7.2.1	Principle of DOP imaging	203
7.2.2	Influence of illumination nonuniformity on segmentation performance	205
7.3	The statistics of the OSCI and its natural representation	206
7.3.1	Speckle and multiplicative noise	207
7.3.2	The probability density function of the OSCI	208
7.3.3	The natural representation of the OSCI	210
7.4	Applications to image processing of the OSCI	212
7.4.1	Target and edge detection	213
7.4.2	Statistical snake segmentation of OSCI	219
7.5	Defining a contrast in Stokes images	223
7.5.1	Position of the problem	223
7.5.2	Contrast parameters for coherent polarimetric signals	225
7.6	Detection and segmentation in Stokes images	227
7.6.1	Target detection/localization	230
7.6.2	Statistical snake-based segmentation	231
7.6.3	Contrast parameters and detection performance	233
7.7	Conclusion	235
7.A	Appendix--Statistical properties of the OSCI	235
7.B	Appendix--GLRT and statistical snake for Gaussian noise with common variance	237
7.C	Appendix--Interpretation of the contrast parameters	238
	Credits	241
	References	243
	Index	253