Potts model parameter estimation in Bayesian segmentation of piecewise constant images

The paper presents a method for estimating the parameter of a Potts model jointly with the unknowns of an image segmentation problem. The method addresses piecewise constant images degraded by additive noise. The proposed solution follows a Bayesian approach, that yields the posterior law for all the unknowns (labels, gray levels, noise level and Potts parameter). It is explored by means of MCMC stochastic sampling, more precisely, by Gibbs algorithm. The estimates are then computed from these samples. The estimation of the Potts parameter is challenging due to the intractable normalizing constant of the model. The proposed solution is based on pre-computing the value of this normalizing constant for different image dimensions and number of classes, this being the novelty of this paper. The segmentation results are as satisfying as those obtained when tuning the parameter by hand.