Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction

Gerhard Winkler (auth.)9783540570691, 3540570691, 0387570691

This second edition of G. Winkler’s successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications. Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required.
The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added.

---

Table of contents :
Front Matter….Pages I-XVI
Introduction….Pages 1-5
Front Matter….Pages 7-7
The Bayesian Paradigm….Pages 9-28
Cleaning Dirty Pictures….Pages 29-53
Finite Random Fields….Pages 55-72
Front Matter….Pages 73-73
Markov Chains: Limit Theorems….Pages 75-112
Gibbsian Sampling and Annealing….Pages 113-128
Cooling Schedules….Pages 129-140
Front Matter….Pages 141-141
Gibbsian Sampling and Annealing Revisited….Pages 143-151
Partially Parallel Algorithms….Pages 153-158
Synchronous Algorithms….Pages 159-175
Front Matter….Pages 177-177
Metropolis Algorithms….Pages 179-196
The Spectral Gap and Convergence of Markov Chains….Pages 197-202
Eigenvalues, Sampling, Variance Reduction….Pages 203-207
Continuous Time Processes….Pages 209-213
Front Matter….Pages 215-215
Partitioning….Pages 217-229
Random Fields and Texture Models….Pages 231-242
Bayesian Texture Classification….Pages 243-248
Front Matter….Pages 249-249
Maximum Likelihood Estimation….Pages 251-261
Consistency of Spatial ML Estimators….Pages 263-280
Computation of Full ML Estimators….Pages 281-298
Front Matter….Pages 299-299
A Glance at Neural Networks….Pages 301-311
Three Applications….Pages 313-323
Back Matter….Pages 325-387