An adaptive Bayesian network for low-level image processing

Probability calculus, based on the axioms of inference, is the only consistent scheme for performing inference; this is also known as Bayesian inference. The objects which this approach manipulates, namely probability density functions (PDFs), may be created in a variety of ways, but the focus of this paper is on the use of adaptive PDF networks. Adaptive mixture distribution (MD) networks are already widely used. In this paper, an extension of the standard MD approach is presented, it is called a partitioned mixture distribution (PMD). PMD networks are designed specifically to scale sensibly to high-dimensional problems, such as image processing. Several numerical simulations are performed, which demonstrate that the emergent properties of PMD networks are similar to those of biological low-level vision processing systems. The use of PDFs as a vehicle for solving inference problems is discussed, and the standard theory of MDs is summarised. The new theory of PMDs is then presented