EM procedures using mean field-like approximations for Markov model-based image segmentation

This paper deals with Markov random eld model-based image segmentation. This involves parameter estimation in hidden Markov models for which one of the most widely used procedures is the EM algorithm. In practice, diiculties arise due to the dependence structure in the models and approximations are required to make the algorithm tractable. We propose a class of algorithms in which the idea is to deal with systems of independent variables. This corresponds to approximations of the pixels' interactions similar to the mean eld approximation. It follows algorithms that have the advantage of taking the Markovian structure into account while preserving the good features of EM. In addition, this class, that includes new and already known procedures, is presented in a uniied framework, showing that apparently distant algorithms come from similar approximation principles. We illustrate the algorithms performance on synthetic and real images. These experiments point out the ability of our procedures to take the spatial information into account. Our algorithms often show signiicant improvement when comparing with the EM algorithm applied with no account of the spatial structure and with the ICM algorithm, based on maximization of the pseudo-likelihood and commonly used in image segmentation. Approximations de type champ moyen pour l'utilisation de l'algorithme EM dans les mod eles markoviens de segmentation d'images R esum e : Cet article traite de l'estimation des param etres d'un champ de Markov cach e pour la segmenta-tion d'images. Dans ce cadre, l'algorithme EM, algorithme de r ef erence pour les mod eles a structure cach ee, se heurte a des diicult es fortes, pour prendre en compte la d ependance spatiale, exigeant des approximations. Nous proposons une classe d'algorithmes fond es sur l'id ee de se ramener a des syst emes de variables ind ependantes. Cela conduit a des approximations de l'interaction des pixels analogues a l'approximation en champ moyen. Nous obtenons ainsi des algorithmes qui prennent en compte la d ependance markovienne tout en conservant les bonnes caract eristiques de l'algorithme EM. Ce point de vue oore un cadre unii e pour des algorithmes d ejj a connus ou nouveaux et permet de montrer que des techniques apparemment bien dii erentes reposent sur des principes d'approximation analogues. Nous illustrons les performances de ces dii erents al-gorithmes sur des images simul ees et r eelles. Ces exp erimentations connrment que nos algorithmes prennent bien en compte les hypoth eses du mod ele de …