Advanced spatial information processes: modeling and application

Making full use of spatial information is an important problem in information-processing and decision making. In this dissertation, two Bayesian decision theoretic frameworks for context classification are developed which make full use of spatial information. The first framework is a new multispectral image context classification technique which is based on a recursive algorithm for optimal estimation of the state of a two-dimensional discrete Markov Random Field (MRF). The implementation of the recursive algorithm is a form of dynamic programming. The second framework is based on a stochastic relaxation algorithm and Markov-Gibbs Random Fields. The relaxation algorithm constitutes an optimization using annealing. We also discuss how to estimate the Markov Random Field Model parameters, which is a key problem in using MRF in image processing and pattern recognition. The estimation of transition probabilities in a 2-D MRF is converted into two 1-D estimation problems. Then a Space-varying estimation method for transition probabilities is discussed.