Image Textures and Gibbs Random Fields

by Georgy L. Gimel'farb

Overview

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 equations, 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.

Product Details

ISBN-13:	9789401059121
Publisher:	Springer Netherlands
Publication date:	10/14/2012
Series:	Computational Imaging and Vision , #16
Edition description:	Softcover reprint of the original 1st ed. 1999
Pages:	251
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

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 Shastic relaxation and shastic 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 Shastic 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.