Pairwise Markov random fields and segmentation of textured images

Abstract

. The use of random fields, which allows one to take into account the spatial interaction among random variables in complex systems, becomes a frequent tool in numerous problems of statistical mechanics, spatial statistics, neural network modelling, and others. In particular, Markov random field based techniques can be of exceptional efficiency in some image processing problems, like segmentation or edge detection. In statistical image segmentation, that we address in this work, the model is generally defined by the probability distribution of the class field, which is assumed to be a Markov field, and the probability distributions of the observations field conditional to the class field. Under some hypotheses, the a posteriori distribution of the class field, i.e. conditional to the observations field, is still a Markov distribution and the latter property allows one to apply different bayesian methods of segmentation like Maximum a Posteriori (MAP) or Maximum of Posterior Mode (MPM). However, in such models the segmentation of textured images is difficult to perform and one has to resort to some model approximations. The originality of our contribution is to consider the markovianity of the couple (class field, observations field). We obtain a different model; in particular, the class field is not necessarily a Markov field. However, the posterior distribution of the class field is a Markov distribution, which makes possible bayesian MAP and MPM segmentations. Furthermore, the model proposed makes possible textured image segmentation with no approximations. Key words: hidden Markov fields, pairwise Markov fields, bayesian image segmentation, textured images. 1.

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