Natural images consist of an overwhelming number of visual patterns generated by very diverse stochastic processes in nature. The objective of image understanding is to parse an input image into its constituent patterns. The figure below is an example of parsing a stadium scene hierarchically: human (face and clothes), sports field (a point process, a curve process, homogeneous color regions, text) and spectators ( textures, persons).

Depending on the type of patterns that a task is interested in, the parsing problem is called respectively

Image segmentation --- for homogeneous grey/color/texture region processes

Perceptual grouping --- for point, curve, and general graph processes

Object recognition --- for text and objects.

Therefore these three traditional vision problems ought to be solved in a unified way, and this can be achieved in a Bayesian framework. Our goal is to develop effective Markov chain Monte Carlo algorithms to search for globally optimal solutions in complex solution spaces. The computation involves both stochastic diffusions by partial differential equations and reversible jumps with Metropolis-Hastings method.

The following is two typical Image parsing examples.

The following is the Diagram integrating generative method (top-down MCMC inference) with discriminative methods (bottom-up, data-driven):