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Random fields and inverse problems in imaging. (English) Zbl 0718.60119
Calcul de probabilités, Éc. d’Été XVIII, Saint-Flour/Fr. 1988, Lect. Notes Math. 1427, 117-193 (1990).
[For the entire collection see Zbl 0708.00013.]
The article is a survey of the use of random fields in imaging problems. The focus is set on Markov random fields and simulated annealing by use of the Metropolis algorithm.
The survey is divided in 6 chapters: 1. Introduction, 2. Random fields on graphs, 3. Stochastic algorithms, 4. Image restoration, 5. Boundary detection, 6. Assorted issues and open problems.
The second chapter is a short presentation of random fields (mainly Markov fields) and various modelisation examples are given. Chapter 3 is mainly devoted to Metropolis ideas and simulated annealing principles. Chapter 4 compares classical methods of restoration with the stochastic ones, and Chapter 5 does the same for the problem of boundaries detection. Chapter 6 treats of parameter estimation and stochastic relaxation and discusses recent progresses in the domain.
The reader needs a serious background in probability theory as well as in mathematical physics.

MSC:
60K40 Other physical applications of random processes
68T10 Pattern recognition, speech recognition
68U10 Computing methodologies for image processing