Texture modeling by multiple pairwise pixel interactions

A Markov random field model with a Gibbs probability distribution (GPD) is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures. The model takes into account only multiple short- and long-range pairwise interactions between the gray levels in the pixels. An effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the GPD as desired parameters. The scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation. Experiments in modeling natural textures show the utility of the proposed model.