When Data Do Not Bring Information: A Case Study in Markov Random Fields Estimation

The Potts model is frequently used to describe the behavior of image classes, since it allows to incorporate contextual information linking neighboring pixels in a simple way. Its isotropic version has only one real parameter β, known as smoothness parameter or inverse temperature, which regulates the classes map homogeneity. The classes are unavailable and estimating them is central in important image processing procedures as, for instance, image classification. Methods for estimating the classes which stem from a Bayesian approach under the Potts model require to adequately specify a value for β. The estimation of such parameter can be efficiently made solving the pseudo maximum-likelihood (PML) equations in two different schemes, using the prior or the posterior model. Having only radiometric data available, the first scheme needs the computation of an initial segmentation, whereas the second uses both the segmentation and the radiometric data to make the estimation. In this paper, we compare these two PML estimators by computing the mean-square error (MSE), bias, and sensitivity to deviations from the hypothesis of the model. We conclude that the use of extra data does not improve the accuracy of the PML; moreover, under gross deviations from the model, this extra information introduces unpredictable distortions and bias.