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

by Gerhard Winkler

Overview

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.

Product Details

ISBN-13:	9783642629112
Publisher:	Springer Berlin Heidelberg
Publication date:	09/22/2012
Series:	Stochastic Modelling and Applied Probability , #27
Edition description:	Second Edition 2003
Pages:	387
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

I. Bayesian Image Analysis: Introduction.- 1. The Bayesian Paradigm.- 2. Cleaning Dirty Pictures.- 3. Finite Random Fields.- II. The Gibbs Sampler and Simulated Annealing.- 4. Markov Chains: Limit Theorems.- 5. Gibbsian Sampling and Annealing.- 6. Cooling Schedules.- III. Variations of the Gibbs Sampler.- 7. Gibbsian Sampling and Annealing Revisited.- 8. Partially Parallel Algorithms.- 9. Synchronous Algorithms.- IV. Metropolis Algorithms and Spectral Methods.- 10. Metropolis Algorithms.- 11. The Spectral Gap and Convergence of Markov Chains.- 12. Eigenvalues, Sampling, Variance Reduction.- 13. Continuous Time Processes.- V. Texture Analysis.- 14. Partitioning.- 15. Random Fields and Texture Models.- 16. Bayesian Texture Classification.- VI. Parameter Estimation.- 17. Maximum Likelihood Estimation.- 18. Consistency of Spatial ML Estimators.- 19. Computation of Full ML Estimators.- VII. Supplement.- 20. A Glance at Neural Networks.- 21. Three Applications.- VIII. Appendix.- A. Simulation of Random Variables.- A.1 Pseudorandom Numbers.- A.2 Discrete Random Variables.- A.3 Special Distributions.- B. Analytical Tools.- B.1 Concave Functions.- B.2 Convergence of Descent Algorithms.- B.3 A Discrete Gronwall Lemma.- B.4 A Gradient System.- C. Physical Imaging Systems.- D. The Software Package AntslnFields.- References.- Symbols.

Editorial Reviews

From the reviews of the second edition:

"This book is concerned with a probabilistic approach for image analysis, mostly from the Bayesian point of view, and the important Markov chain Monte Carlo methods commonly used in this approach. … this book will be useful, especially to researchers with a strong background in probability and an interest in image analysis. The author has presented the theory with rigor … . he doesn’t neglect applications, providing numerous examples of applications to illustrate the theory and an abundant bibliography pointing to more detailed related work." (Pham Dinh Tuan, Mathematical Reviews, Issue 2004 c)

"Based on the Baysian approach the author focuses on the principles of classical image analysis rather than on applications and implementations. Little mathematical knowledge is needed to read the book, thus it is well suited for lectures on image analysis." (Ch. Cenker, Monatshefte für Mathematik, Vol. 146 (4), 2005)

From the Publisher