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© 2003

Image Analysis, Random Fields and Markov Chain Monte Carlo Methods

A Mathematical Introduction

Book

Part of the Applications of Mathematics book series (SMAP, volume 27)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Introduction

    1. Gerhard Winkler
      Pages 1-5
  3. Bayesian Image Analysis: Introduction

    1. Front Matter
      Pages 7-7
    2. Gerhard Winkler
      Pages 9-28
    3. Gerhard Winkler
      Pages 29-53
    4. Gerhard Winkler
      Pages 55-72
  4. The Gibbs Sampler and Simulated Annealing

    1. Front Matter
      Pages 73-73
    2. Gerhard Winkler
      Pages 75-112
    3. Gerhard Winkler
      Pages 113-128
    4. Gerhard Winkler
      Pages 129-140
  5. Variations of the Gibbs Sampler

    1. Front Matter
      Pages 141-141
    2. Gerhard Winkler
      Pages 143-151
    3. Gerhard Winkler
      Pages 153-158
    4. Gerhard Winkler
      Pages 159-175
  6. Metropolis Algorithms and Spectral Methods

    1. Front Matter
      Pages 177-177
    2. Gerhard Winkler
      Pages 179-196
    3. Gerhard Winkler
      Pages 203-207
    4. Gerhard Winkler
      Pages 209-213
  7. Texture Analysis

    1. Front Matter
      Pages 215-215

About this book

Introduction

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.

Keywords

Bayesian statistics Estimator Likelihood Markov chain Monte Carlo methods Partition Random variable Simulation Textur Variance calculus classification image analysis random fields spatial modeling statistical image analysis

Authors and affiliations

  1. 1.IBB — Institute of Biomathematics and BiometryGSF — National Research Centre for Environment and HealthNeuherberg/MünchenGermany

Bibliographic information

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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)