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 segmentation, and synthesis of data. While there are several approaches available for texture modeling, the research presented here is concerned with stochastic texture models. Stochastic approaches view a texture as the realization 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 Markov models (POMMs). Markov random fields are a class of stochastic models that incorporate spatial dependency between data points. One major disadvantage of MRFs is that, in general, an explicit form of the joint probability of the random variables describing the model is not obtainable. However, a popular subclass of MRFs, called Markov mesh models (MMMs), allows the explicit description of the joint probability in terms of spatially local conditional probabilities. We show how POMMs are a generalization of MMMs and demonstrate the versatility of POMMs to texture synthesis and pattern recognition in imaging. Specifically, we give a fast, one-pass algorithm for simulating textures using POMMs, and introduce examples of heterogeneous models that suggest potential applications for object recognition purposes. Then we address an inverse problem, where we present results from a series of statistical experiments designed to estimate parameters of stochastic texture models for both binary and gray value data. Although the applications in this 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 Recognition Society. Published by Elsevier Science Ltd. All rights reserved.