Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields

Abstract

The modeling and segmentation of images by MRF's (Markov random fields) is treated. These are two-dimensional noncausal Markovian stochastic processes. Two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of C MRF's. The algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology. A doubly stochastic representation is used in image modeling. Here, a Gaussian MRF is used to model textures in visible light and infrared images, and an autobinary (or autoternary, etc.) MRF to model a priori information about the local geometry of textured image regions. For image segmentation, the true texture class regions are treated either as a priori completely unknown or as a realization of a binary (or ternary, etc.) MRF. In the former case, image segmentation is realized as true maximum likelihood estimation. In the latter case, it is realized as true maximum a posteriori likelihood segmentation. In addition to providing a mathematically correct means for introducing geometric structure, the autobinary (or ternary, etc.) MRF can be used in a generative mode to generate image geometries and artificial images, and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters. The first segmentation algorithm is hierarchical and uses a pyramid-like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region.