Shape Modeling and Object Recognition

Shape modeling is to represent generic object geometry by a number of models which account for the regularity and variablity of natural objects. Shape modeling is the fundation for object recognition under change of pose, deformation, and varying lighting coditions. However, this is an extremely hard problem, and most of the mathematical studies appear to be totally irrelevant to natural object shape description. Key questions are:

1. What are the domain or coordinates for shape description? In what mathematical spaces do natural shape live?

2. How do we define a meaningful metric (distance measure) in such space?

3. There is no distinct boundary between shape and texture, can we construct shape models living in a continuous spectrum of texture models?

The recent study of texture theory indeed shed light on shape modeling, and we feel these problems can be answered in near future. In our group, we made four attempts to study shape models, mostly on 2D outlines of objects. We are planning for the 5th project on shape sketch which works on both contour and inner curves.

1. FORMS: a Flexible Object Recognition and Modeling System, 1993-95 ---a generative region-based shape model.

2. Stochastic medial axis and Gestalt laws in Markov random fields, 1997-98 --- a descriptive shape model.

3. Shape representation by a sum of linear bases 2000-02 --- a contour-based linear additive model.

4. A sketch model of shape 02-?? --- a generative model integrating both contour and region based descriptor.

5. Shape metrics and morphing 02--??

Outside our group, there are many good work by David Cooper, Ben Kimia, David Mumford and Peter Giblin at Brown University.