Local neighborhood transition probability estimation and its use in contextual classification

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.