Pairwise Markov random fields and segmentation

The use of random elds, 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 eld based techniques can be of exceptional eeciency in some image processing problems, like segmen-tation or edge detection. In statistical image segmentation, that we address in this work, the model is generally deened by the probability distribution of the class eld, which is assumed to be a Markov eld, and the probability distributions of the observations eld conditional to the class eld. Under some hypotheses, the a posteriori distribution of the class eld, i.e. conditional to the observations eld, is still a Markov distribution and the latter property allows one to apply diierent 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 diicult 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 eld, observations eld). We obtain a diierent model; in particular, the class eld is not necessarily a Markov eld. However, the posterior distribution of the class eld is a Markov distribution, which makes possible bayesian MAP and MPM segmentations. Furthermore, the model proposed makes possible textured image segmentation with no approximations.