On the statistical analysis of dirty pictures (with discussion). (English) Zbl 0609.62150

Besag, Julian

J. R. Stat. Soc., Ser. B 48, 259-302 (1986).

This paper contains an extensive treatment of a statistical analysis of pictures corrupted by noises. A picture is viewed as a two-dimensional region consisting of ”n” pixels where each of them takes one of ”c” colours. The aim is to reconstruct the true picture on the basis of information conveyed by a picture imposed by noises. A main assumption behind the methods of picture reconstruction discussed here deals with a nondegenerate Markov random field for representation of local characteristics of the picture. Also some links to Geman and Geman’s solution of the problem via simulated annealing are underlined.
Simple iterative methods for picture reconstruction (an algorithm of iterated conditional modes) are analyzed and numerical examples (artificial pictures) are given. They are compared with maximum likelihood classifiers. Moreover, broader classes of Markov random fields useful for different types of scenes (unordered colours, grey-level scenes) are introduced. The paper is enriched by a discussion dealing with the role of statistics and its use for picture restoration.

Reviewer: W.Pedrycz

MSC:

62P99	Applications of statistics
62H30	Classification and discrimination; cluster analysis (statistical aspects)
68T10	Pattern recognition, speech recognition

Keywords:

pattern recognition; remote sensing; grey-level scenes; pseudo-likelihood estimation; image processing; pixels; picture reconstruction; Markov random field; simulated annealing; algorithm of iterated conditional modes; maximum likelihood classifiers; picture restoration