Experiments in Filtering Discrete Markov Random Fields to Textures

Abstract

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- chi /sup 2/ 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>