Winkler, G: Image Analysis, Random Fields and Dynamic Monte

en Limba Engleză Paperback – 19 ian 2012

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.

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Cuprins

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.

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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.