The Partitioned Mixture Distribution: An Adaptive Bayesian Network for Low- Level Image Processing

Bayesian methods are used to analyse the problem of training a model to make predictions about the probability distribution of data that has yet to be received. Mixture distributions emerge naturally from this framework, but are not well-matched to highdimensional problems such as image processing. An extension, called a partitioned mixture distribution (PMD) is presented, which is essentially a set of overlapping mixture distributions. An expectation-maximisation training algorithm is derived. Finally, the results of some numerical simulations are presented, which demonstrate that lateral inhibition arises naturally in PMDs, and that the nodes in a PMD co-operate in such a way that each mixture distribution in the PMD receives the necessary complement of machinery for it to compute its mixture distribution.