A Mathematical Theory of Primal Sketch and Sketchability


Ying Nian Wu
UCLA Department of Statistics

Time: Friday 28 March 10:15-11:00 am
Place: N014 DIKU


Walking in Copenhagen in the early Spring and looking at the trees, we can easily notice a scaling phenomenon. For the trees far from us, the twigs, branches only give us a texture impression, and they are non-sketchable. But for the trees close to us, we can notice the individual branches and twigs, and they become sketchable. While the change of the retina image with distance can be accounted by continuous scale-space theory, our perception in V1 experiences a quantum jump between sketchable and non-sketchable. This sketchability phenomenon is ubiquitous in natural scenes.

In this talk, I will present a mathematical theory for Marr's primal sketch. The central piece of the theory is a primal sketch model, where the sketchable part of the image is represented by the constructive scheme of sparse coding, whereas the non-sketchable part of the image is represented by the restrictive scheme of Markov random field. The theory reveals the two complexity regimes for the two classes of patterns and modeling schemes, and suggests the role of V1 cells as both linear filters without lateral inhibition and linear bases with lateral inhibition. A large number of natural images can be modeled by our theory.

Based on joint work with C. Guo and S. C. Zhu.