Numerical computation with Bayesian posterior densities has recently received much attention both in the applied statistics and image processing communities. This paper surveys previous literature and presents efficient methods for computing marginal density values for image models that have been widely considered in computer vision and image processing. The particular models chosen are a Markov random field (MRF) formulation, implicit polynomial surface models, and parametric polynomial surface models. The computations can be used to make a variety of statistically based decisions, such as assessing region homogeneity for segmentation or performing model selection. Detailed descriptions of the methods are provided, along with demonstrative experiments on real imagery.

Clustering methods, which are frequently employed for region-based segmentation, are inherently metric based. A fundamental problem with an estimation-based criterion is that as the amount of information in a region decreases, the parameter estimates become extremely unreliable and incorrect decisions are likely to be made. It is shown that clustering need not be metric based. A rigorous region merging probability function is used. It makes use of all information available in the probability densities of a statistical image model. By using this probability function as a termination criterion it is possible to produce segmentations in which all region merges are performed above some level of confidence.>