Inference strategies for the smoothness parameter in the Potts model

The Potts model is a commonplace in Bayesian image analysis since its introduction as a convenient image prior. It is able to describe the distribution of classes, yielding a regularization term in the cost function to be minimized in many classification problems. The simplest isotropic version depends on a scalar smoothness parameter; its value controls the relative influence of the regularization with respect to the data. This work analyzes the performance of two pseudolike-lihood estimation procedures of the smoothness parameter of the Potts model: the classical one, which employs the map of classes, and a new estimator based on the posterior distribution, which also incorporates the evidence provided by the observed data. Our simulation study shows that the combination of prior information and observation data gives accurate β estimations when true data is provided. We also discuss its influence in the classification results when comparing contextual ICM (Iterated Conditional Modes) classification experiments with multispectral optical imagery, estimating the scalar parameter β with our estimator and the classical one. Our experiment shows promising results, since ICM with our estimator is able to distinguish image features that the classical ICM does not.