Model selection and texture segmentation using partially ordered Markov models

Texture is a phenomenon in image data that continues to receive attention due to its wide-spread applications, ranging from remotely sensed data, to medical imaging, to military applications. We use a new class of spatial stochastic models called partially ordered Markov models (POMMs) for texture analysis and model selection. POMMs are a generalization of Markov mesh models that have the property that their joint probability density function is an exact, closed form expression in terms of conditional probabilities. Markov random fields (MRFs) do not, in general, have this property. This property of the POMMs has lead to exact and fast computations involving the joint probabilities. We show how these fast algorithms allow POMMs to be used for fitting models to textures, and for supervised texture segmentation. Applications to real data show that the model selection technique gives very good results. POMMs are a broad and general class of models, and have the potential to be applied to diverse areas beyond imaging, such as probabilistic expert systems and artificial intelligence