A Markov random fields model for describing unhomogeneous textures: generalized random stereograms

We consider a stochastic interpretation of textures composed of textural elements that may not obey any particular ordering relation between them. Two-dimensional Markov random fields (MRF) model is proposed to describe the stochastic character of texture patterns. For a fixed lattice we show how unhomogeneous textures can be described. We discuss the evidence of phase transitions in generating such textures. Distance relation based on joint entropy is proposed to measure the statistical interdependence between random variables assigned to the nodes of the two-dimensional network. The form of this function is shown to be suitable as an objective measure of phase transitions when distinct texture regions evolve while cooling "temperature". The examples of unhomogeneous (figure-ground) type of textures which we call generalized random stereograms are used to illustrate the model. We discuss the relevance of the model for generating texture patterns for neurophysiological experiments, psychophysical experiments and pattern recognition.<>