Image Analysis, Random Fields and Dynamic Monte Carlo Methods

1. Front Matter

   Pages I-XIV

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2. Introduction

   1. Introduction

      • Gerhard Winkler

      Pages 1-9

3. Bayesian Image Analysis: Introduction

   1. Front Matter

      Pages 11-11

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   2. The Bayesian Paradigm

      • Gerhard Winkler

      Pages 13-22

   3. Cleaning Dirty Pictures

      • Gerhard Winkler

      Pages 23-46

   4. Random Fields

      • Gerhard Winkler

      Pages 47-61

4. The Gibbs Sampler and Simulated Annealing

   1. Front Matter

      Pages 63-63

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   2. Markov Chains: Limit Theorems

      • Gerhard Winkler

      Pages 65-79

   3. Sampling and Annealing

      • Gerhard Winkler

      Pages 81-98

   4. Cooling Schedules

      • Gerhard Winkler

      Pages 99-112

   5. Sampling and Annealing Revisited

      • Gerhard Winkler

      Pages 113-129

5. More on Sampling and Annealing

   1. Front Matter

      Pages 131-131

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   2. Metropolis Algorithms

      • Gerhard Winkler

      Pages 133-154

   3. Alternative Approaches

      • Gerhard Winkler

      Pages 155-166

   4. Parallel Algorithms

      • Gerhard Winkler

      Pages 167-191

6. Texture Analysis

   1. Front Matter

      Pages 193-193

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   2. Partitioning

      • Gerhard Winkler

      Pages 195-208

   3. Texture Models and Classification

      • Gerhard Winkler

      Pages 209-221

7. Parameter Estimation

   1. Front Matter

      Pages 223-223

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   2. Maximum Likelihood Estimators

      • Gerhard Winkler

      Pages 225-235

This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.

• Markov Random Field
• Monte Carlo
• Monte Carlo method
• Monte Carlos Methods
• Probability theory
• algorithms
• image analysis
• imaging
• statistics

• Mathematical Institute, Ludwig-Maximilians Universität, München, Germany

  Gerhard Winkler

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