Summary of Research Streams and Unification

---- a big picture

    This is not an intent for a complete survey of texture work, instead it
is a summary of research streams. It is interesting and amazing to see that
how many disciplines have contributed to our understanding of textures. 
Actually a bigger picture is emerging from recent studies. A survey paper is
referred to 
  S.C. Zhu, "Statistical modeling and conceptualization of vision patterns",
Submitted to IEEE Trans on PAMI. A short version appeared in IEEE Workshop 
on Perceptual Organization in Computer Vision, Vancouver, July 2001.
  Basically these research streams can be summarized into 4 categories of 
statistical models, and these models can be understood in a unified framework.

The figure above illustrates the four types of models for representing a "table" with a table top and four legs. A descriptive model imposes statistical constraints on the relationships of tops and legs, and such statistical description is turned into a Gibbs (MRF) model by maximum entropy. A causal MRF model is a special case of descriptive model by imposing a partial order among the nodes. Thus it is an approximation to the Gibbs models. The generative model introduces hidden variable for the concept of a table. Thus the parts of the table become less dependent under the condition of the hidden variable. The discriminative model is an approximation to the posterior, and it can only provide computational heuristics, expressed as importance proposal probabilities.