Texton, Gestalt, and Perceptual Organization
  Natural images contains a broad spectrum of stochastic visual patterns, such as texture, point, 
line, curve, graph processes, and geometry and shape.  Developing mathematical models of these
 patterns is of crucial importance for building general purpose and robust vision systems. 

  In general,  we have two observations:

1. The spectrum of patterns should be continuous.  Thus models for texture up to geometry should form
   a nested family and be compatible.  The visual patterns vary from each other in two aspects:

   a). What are the basic elements (paricles)?  pixels, wavelet bases, textons, lines, curves, 
                 junctions, up to geometric descriptions: spline bases, meaningful parts.
                 Evidently, the definition of elements, such as "textons", "meaningful parts"
                 must be governed by proper mathematical models of the whole pattern.

   b). What are the potential functions characterizing the interactions among elements?
                 In statistical mechanics, a stochastic pattern is modeled by a Gibbs distribution
                 with potentials defined on a neighborhood system.  Then other intuitive physical
                 concepts can be derived, such as "forces", "diffusion", et al.
                 Of course, a natural question arises: how do we define a good neighborhood system?

2. Models of visual patterns should be learned from observations.

   a). We must use generative models which naturally reflect the hierarchic organization of particles.

   b). Descriptive models are the precursors of generative model.

   Descriptive models can be learned from a minimax entropy learning theory, and generative models
   are learned through EM-type algorithm and it integrates the minimax entropy learning.


We are making the following attempts in studying the problems:

1. What is texton I ? --- discovering textons by a generative model.

2. What is texton II? --- from wavelet bases to texton.(*updated)

3. Gestalt ensemble: --- conceptualization and modeling of texton processes.

4. An integrated learning paradigm.

5. Stochastic line, curve, and graph processes.

6. Shape Modeling