Texture synthesis and pattern recognition for partially ordered Markov models

The uses of texture in image analysis are widespread, ranging from remotely sensed data to medical imaging to military applications. Image processing tasks that use texture characteristics include classification, region segme ntation, and synthesis of data. While there are several approaches availabl e for texture modeling, the research presented here is concerned with stoch astic texture models. Stochastic approaches view a texture as the realizati on of a random field and are most useful when the texture appears noisy or when it lacks smooth geometric features. The model introduced in this paper is a subclass of Markov random fields (MRFs) called partially ordered Mark ov models (POMMs). Markov random fields are a class of stochastic models th at incorporate spatial dependency between data points. One major disadvanta ge of MRFs is that, in general, an explicit form of the joint probability o f the random variables describing the model is not obtainable. However, a p opular subclass of MRFs, called Markov mesh models (MMMs), allows the expli cit description of the joint probability in terms of spatially local condit ional probabilities. We show how POMMs are a generalization of MMMs and dem onstrate the versatility of POMMs to texture synthesis and pattern recognit ion in imaging. Specifically, we give a fast, one-pass algorithm for simula ting textures using POMMs, and introduce examples of heterogeneous models t hat suggest potential applications for object recognition purposes. Then we address an inverse problem, where we present results from a series of stat istical experiments designed to estimate parameters of stochastic texture m odels for both binary and gray value data. Although the applications in thi s paper focus on imaging, in their most general form, POMMs can be found in areas such as probabilistic expert systems, Bayesian hierarchical modeling , influence diagrams, and random graphs and networks. (C) 1999 Pattern Reco gnition Society. Published by Elsevier Science Ltd. All rights reserved.