© 1995

Image Analysis, Random Fields and Dynamic Monte Carlo Methods

A Mathematical Introduction


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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Introduction

    1. Gerhard Winkler
      Pages 1-9
  3. Bayesian Image Analysis: Introduction

    1. Front Matter
      Pages 11-11
    2. Gerhard Winkler
      Pages 13-22
    3. Gerhard Winkler
      Pages 23-46
    4. Gerhard Winkler
      Pages 47-61
  4. The Gibbs Sampler and Simulated Annealing

    1. Front Matter
      Pages 63-63
    2. Gerhard Winkler
      Pages 65-79
    3. Gerhard Winkler
      Pages 81-98
    4. Gerhard Winkler
      Pages 99-112
    5. Gerhard Winkler
      Pages 113-129
  5. More on Sampling and Annealing

    1. Front Matter
      Pages 131-131
    2. Gerhard Winkler
      Pages 133-154
    3. Gerhard Winkler
      Pages 155-166
    4. Gerhard Winkler
      Pages 167-191
  6. Texture Analysis

    1. Front Matter
      Pages 193-193
    2. Gerhard Winkler
      Pages 195-208
    3. Gerhard Winkler
      Pages 209-221
  7. Parameter Estimation

    1. Front Matter
      Pages 223-223
    2. Gerhard Winkler
      Pages 225-235

About this book


The book is mainly concerned with the mathematical foundations of Bayesian image analysis and its algorithms. This amounts to the study of Markov random fields and dynamic Monte Carlo algorithms like sampling, simulated annealing and stochastic gradient algorithms. The approach is introductory and elemenatry: given basic concepts from linear algebra and real analysis it is self-contained. No previous knowledge from image analysis is required. Knowledge of elementary probability theory and statistics is certainly beneficial but not absolutely necessary. The necessary background from imaging is sketched and illustrated by a number of concrete applications like restoration, texture segmentation and motion analysis.


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

Authors and affiliations

  1. 1.Mathematical InstituteLudwig-Maximilians UniversitätMünchenGermany

Bibliographic information

Industry Sectors
IT & Software
Finance, Business & Banking
Energy, Utilities & Environment
Oil, Gas & Geosciences