Pairwise Markov random fields and its application in textured images segmentation

The use of random fields, which allows one to take into account the spatial interaction among random variables in complex systems, is a frequent tool in numerous problems of statistical image processing, like segmentation or edge detection. In statistical image segmentation, 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. 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 pair (class field observations field). We obtain a different model; in particular, the class field is not necessarily a Markov field. The model proposed makes possible the use of Bayesian methods like MPM or MAP to segment textured images with no model approximations. In addition, the textured images can be corrupted with correlated noise. Some first simulations to validate the model proposed are also presented.