Image Textures and Gibbs Random Fields

Image analysis is one of the most challenging areas in today's computer sci ence, and image technologies are used in a host of applications. This book concentrates on image textures and presents novel techniques for their sim ulation, retrieval, and segmentation using specific Gibbs random fields with multiple pairwise interaction between signals as probabilistic image models. These models and techniques were developed mainly during the previous five years (in relation to April 1999 when these words were written). While scanning these pages you may notice that, in spite of long equa tions, the mathematical background is extremely simple. I have tried to avoid complex abstract constructions and give explicit physical (to be spe cific, "image-based") explanations to all the mathematical notions involved. Therefore it is hoped that the book can be easily read both by professionals and graduate students in computer science and electrical engineering who take an interest in image analysis and synthesis. Perhaps, mathematicians studying applications of random fields may find here some less traditional, and thus controversial, views and techniques.

Texte du rabat

This book presents novel techniques for describing image textures. Contrary to the usual practice of embedding the images to known modelling frameworks borrowed from statistical physics or other domains, this book deduces the Gibbs models from basic image features and tailors the modelling framework to the images. This approach results in more general Gibbs models than can be either Markovian or non-Markovian and possess arbitrary interaction structures and strengths. The book presents computationally feasible algorithms for parameter estimation and image simulation and demonstrates their abilities and limitations by numerous experimental results. The book avoids too abstract mathematical constructions and gives explicit image-based explanations of all the notions involved. Audience: The book can be read by both specialists and graduate students in computer science and electrical engineering who take an interest in texture analysis and synthesis. Also, the book may be interesting to specialists and graduate students in applied mathematics who explore random fields.

Contenu
Instead of introduction.- 1 Texture, Structure, and Pairwise Interactions.- 1.1 Human and computational views.- 1.2 Spatial homogeneity, or self-similarity of textures.- 1.3 Basic notation and notions.- 1.4 Random fields and probabilistic image modelling.- 1.5 Physics and image modelling: what an interaction means.- 1.6 GPDs and exponential families of distributions.- 1.7 Stochastic relaxation and stochastic approximation.- 2 Markov and Non-Markov Gibbs Image Models.- 2.1 Traditional Markov/Gibbs image models.- 2.2 Generalized Gibbs models of homogeneous textures.- 2.3 Prior Markov/Gibbs models of region maps.- 2.4 Piecewise-homogeneous textures.- 2.5 Basic features of the models.- 3 Supervised MLE-Based Parameter Learning.- 3.1 Affine independence of sample histograms.- 3.2 MLE of Gibbs potentials.- 3.3 Analytic first approximation of potentials.- 3.4 Most characteristic interaction structure.- 3.5 Stochastic approximation to refine potentials.- 4 Supervised Conditional MLE-Based Learning.- 4.1 The least upper bound condition.- 4.2 Potentials in analytic form.- 4.3 Practical consistency of the MLEs.- 5 Experiments in Simulating Natural Textures.- 5.1 Comparison of natural and simulated textures.- 5.2 Brodatz image database.- 5.3 Interaction maps and texture features.- 5.4 CSA vs. traditional modelling scenario.- 5.5 MIT VisTex image database.- 6 Experiments in Retrieving Natural Textures.- 6.1 Query-by-image texture retrieval.- 6.2 Similarity under scale and orientation variations.- 6.3 Matching two textures.- 6.4 Experiments with natural textures.- 6.5 Complexity and practicality.- 7 Experiments in Segmenting Natural Textures.- 7.1 Initial and final segmentation.- 7.2 Artificial collages of Brodatz textures.- 7.3 Natural piecewise-homogeneous images.- 7.4How to choose an interaction structure.- 7.5 Do Gibbs models learn what we expect?.- Texture Modelling: Theory vs. Heuristics.- References.