Maximum marginal likelihood estimation of the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts-Markov random field parameter β jointly with the unknown parameters of a Bayesian image segmentation model. We propose a new adaptive Markov chain Monte Carlo (MCMC) algorithm for performing joint maximum marginal likelihood estimation of β and maximum-a-posteriori unsupervised image segmentation. The method is based on a stochastic gradient adaptation technique whose computational complexity is significantly lower than that of the competing MCMC approaches. This adaptation technique can be easily integrated to existing MCMC methods where β was previously assumed to be known. Experimental results on synthetic data and on a real 3D real image show that the proposed method produces segmentation results that are as good as those obtained with state-of-the-art MCMC methods and at much lower computational cost.