Partitioned mixture distribution: an adaptive Bayesian network for low-energy 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 ideally matched to the density estimation problems that arise in image processing. An extension, called a partitioned mixture distribution is presented, which is essentially a set of overlapping mixture distributions. An expectation maximisation training algorithm is derived for optimising partitioned mixture distributions according to the maximum likelihood description. Finally, the results of some numerical simulations are presented, which demonstrate that lateral inhibition arises naturally in partitioned mixture distributions, and that the nodes in a partitioned mixture distribution network co-operate in such a way that each mixture distribution in the partitioned mixture distribution receives its necessary complement of computing machinery.