9780792359616

Presents novel techniques for describing image textures. Presents computationally feasible algorithms for parameter estimation and image simulation, demonstrating their abilities and limitations by numerous experimental results.

Preface

ix

Acknowledgements

xiii

Instead of introduction

1

(4)

Texture, Structure, and Pairwise Interactions

5

(32)

Human and computational views

5

(3)

Spatial homogeneity, or self-similarity of textures

8

(2)

Basic notation and notions

10

(4)

Random fields and probabilistic image modelling

14

(6)

Neighborhoods and Markov random fields

15

(2)

Gibbs probability distributions

17

(2)

Tradeoffs between Gibbs and Markov fields

19

(1)

Physics and image modelling: what an interaction means

20

(4)

GPDs and exponential families of distributions

24

(4)

Stochastic relaxation and stochastic approximation

28

(9)

General features of stochastic relaxation

29

(2)

Stochastic approximation

31

(2)

Pixelwise stochastic relaxation

33

(4)

Markov and Non-Markov Gibbs Image Models

37

(26)

Traditional Markov/Gibbs image models

37

(8)

Auto-binomial and Gauss/Markov models

38

(5)

Models with multiple pairwise interactions

43

(2)

Generalized Gibbs models of homogeneous textures

45

(6)

Non-Markov Gibbs image model

45

(2)

Markov/Gibbs model

47

(1)

Simplified non-Markov model

48

(1)

Exponential family representations

49

(1)

GLH, GLDH, and a few less famous abbreviations

50

(1)

Prior Markov/Gibbs models of region maps

51

(3)

Piecewise-homogeneous textures

54

(6)

Joint model of grayscale images and region maps

55

(2)

Conditional models of images and region maps

57

(3)

Basic features of the models

60

(3)

Supervised MLE-Based Parameter Learning

63

(38)

Affine independence of sample histograms

63

(4)

Gibbs model of homogeneous textures

64

(2)

Gibbs model of region maps

66

(1)

MLE of Gibbs potentials

67

(3)

Analytic first approximation of potentials

70

(2)

Most characteristic interaction structure

72

(12)

Model-based interaction map

72

(2)

Interaction maps and Gibbs potentials

74

(2)

Recovering the interaction structure

76

(8)

Stochastic approximation to refine potentials

84

(17)

Alternative scenario of texture modelling

90

(8)

Controllable simulated annealing

98

(1)

Texture simulation and segmentation

99

(2)

Supervised Conditional MLE-Based Learning

101

(10)

The least upper bound condition

101

(2)

Potentials in analytic form

103

(2)

First approximation of scaling factors

104

(1)

Search for the interaction structure

105

(1)

Stochastic approximation to refine factors

105

(1)

Practical consistency of the MLEs

105

(6)

Signal combinations in the cliques

106

(1)

Potential approximation and interpolation

106

(5)

Experiments in Simulating Natural Textures

111

(34)

Comparison of natural and simulated textures

111

(6)

``Brodatz'' image database

117

(2)

Interaction maps and texture features

119

(4)

CSA vs. traditional modelling scenario

123

(3)

``MIT VisTex'' image database

126

(19)

Experiments in Retrieving Natural Textures

145

(38)

Query-by-image texture retrieval

146

(1)

Similarity under scale and orientation variations

147

(4)

Size of a texture

148

(1)

Texture similarity measure

149

(2)

Matching two textures

151

(2)

Experiments with natural textures

153

(21)

Image data base IDB-1

153

(15)

Image data base IDB-2

168

(6)

Complexity and practicality

174

(9)

Experiments in Segmenting Natural Textures

183

(56)

Initial and final segmentation

183

(1)

Artificial collages of Brodatz textures

184

(23)

Five-region collage

184

(1)

Different four-region collages

184

(12)

Collage of 16 textures

196

(11)

Natural piecewise-homogeneous images

207

(13)

Discrimination of landforms

207

(8)

Grayscale images of the Earth's surface

215

(5)

How to choose an interaction structure

220

(12)

Three variants of a choice

220

(4)

Impact of chosen structures on segmentation

224

(8)

Do Gibbs models learn what we expect?

232

(7)

Texture Modelling: Theory vs. Heuristics

239

(4)

References

243

(6)

Index

249

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Image Textures and Gibbs Random Fields

0792359615

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