Double Markov random fields and Bayesian image segmentation

Markov random fields are used extensively in model-based approaches to image segmentation and, under the Bayesian paradigm, are implemented through Markov chain Monte Carlo (MCMC) methods. We describe a class of such models (the double Markov random field) for images composed of several textures, which we consider to be the natural hierarchical model for such a task. We show how several of the Bayesian approaches in the literature can be viewed as modifications of this model, made in order to make MCMC implementation possible. From a simulation study, conclusions are made concerning the performance of these modified models.