Experiments in filtering discrete Markov random fields to textures

The authors examine two important problems, estimation and goodness of fit, in modeling binary single-texture images by discrete Markov random fields. A methodology for comparing parameter estimators is proposed and applied to evaluate four estimation procedures. The classes of models considered are four-parameter Derin-Elliot models and four-parameter autobinomial models with second-order neighborhoods. A Min-χ² estimator is proposed and shown to outperform estimators described in the literature. The methodology is based on a hardcore sampling process over the parameter space and a Wilcoxon rank-sum statistic. A static for assessing the goodness of fit between a specific model and an arbitrary texture image is also proposed and used in a Monte Carlo ranking test. The statistic is experimentally validated on synthetic textures. Experiments on natural textures suggest that second-order binary models do not fit natural textures well