Methods for numerical integration of high-dimensional posterior densities with application to statistical image models

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.