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On the Equivalence of Regular Grammars and Stochastic Constraints: Applications to Image Processing on Massively Parallel Processors

Michael I. Miller, Badrinath Roysam, Kurt Smith and Jan Tijmen Udding
Lecture Notes-Monograph Series
Vol. 20, Spatial Statistics and Imaging (1991), pp. 239-257
Stable URL: http://www.jstor.org/stable/4355709
Page Count: 19
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On the Equivalence of Regular Grammars and Stochastic Constraints: Applications to Image Processing on Massively Parallel Processors
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Abstract

In this paper we propose a general method for mapping regular grammars to their equivalent stochastic representations, thereby allowing for a unified solution of stochastic estimation and or statistical pattern recognition problems over rule generated constraint spaces. For current problems in image processing in which features of the images are described by deterministic rules, and the measurements from which the images are reconstructed are samples of a probability distribution, such a synthesis is absolutely invaluable. The basic approach taken is to establish the formal connection of rules to Chomsky grammars, and to generalize the original work of Shannon on encoding rule-based channel sequences in Markov chains of the same entropy. Coupling these results to the stochastic diffusions algorithms which sample these Gibbs distributions, yields the all important practical results that highly parallel computers may be used to sample the rule-constrained sets. We present results for image segmentation and reconstruction for emission tomography based on the DAP 510 mesh connected SIMD processor of Active Memory Technology.

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