Morphologically constrained GRFs: applications to texture synthesis and analysis

A new class of Gibbs random fields (GRFs) is proposed capable of modeling geometrical constraints in images by means of mathematical morphology. The proposed approach, known as morphologically constrained GRFs, models images by means of their size density. Since the size density is a multiresolution statistical summary, morphologically constrained GRFs explicitly incorporate multiresolution information into image modeling. Important properties are studied and their implication to texture synthesis and analysis is discussed. Statistical inference can be easily implemented by means of mathematical morphology. This allows the design of a computationally simple morphological Bayes classifier which produces excellent results in classifying natural textures.