Image Analysis, Random Fields and Dynamic Monte Carlo Methods

A Mathematical Introduction

Gerhard Winkler (Autor)

Buch | Softcover

XIV, 324 Seiten

2012
Springer Berlin (Verlag)
9783642975240 (ISBN)

Infos

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.

Autor

The text presents Bayesian image analysis and dynamic Monte Carlo algorithms from the mathematical point of view. The subject is introduced at a moderate pace and the proofs are thorough. Specific models are developed step by step and discussed.

Inhalt

I. Bayesian Image Analysis: Introduction.- 1. The Bayesian Paradigm.- 2. Cleaning Dirty Pictures.- 3. Random Fields.- II. The Gibbs Sampler and Simulated Annealing.- 4. Markov Chains: Limit Theorems.- 5. Sampling and Annealing.- 6. Cooling Schedules.- 7. Sampling and Annealing Revisited.- III. More on Sampling and Annealing.- 8. Metropolis Algorithms.- 9. Alternative Approaches.- 10. Parallel Algorithms.- IV. Texture Analysis.- 11. Partitioning.- 12. Texture Models and Classification.- V. Parameter Estimation.- 13. Maximum Likelihood Estimators.- 14. Spacial ML Estimation.- VI. Supplement.- 15. A Glance at Neural Networks.- 16. Mixed Applications.- VII. Appendix.- A. Simulation of Random Variables.- B. The Perron-Frobenius Theorem.- C. Concave Functions.- D. A Global Convergence Theorem for Descent Algorithms.- References.

Produkt-Details

• Erscheint lt. Verlag: 19.1.2012
• Reihe/Serie: Stochastic Modelling and Applied Probability
• Zusatzinfo: XIV, 324 p.
• Verlagsort: Berlin
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 516 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: algorithms • Image Analysis • Imaging • markov random field • Monte Carlo • Monte Carlo Method • Monte Carlos Methods • Probability Theory • Statistics
• ISBN-13: 9783642975240 / 9783642975240
• Zustand: Neuware