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Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields
February 1987 (vol. 9 no. 2)
pp. 195-219
Fernand S. Cohen, Department of Electrical Engineering, University of Rhode Island, Kingston, RI 02881.
David B. Cooper, Division of Engineering, Brown University, Providence, RI 02912.
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.
Fernand S. Cohen, David B. Cooper, "Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 9, no. 2, pp. 195-219, Feb. 1987, doi:10.1109/TPAMI.1987.4767895
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