# A Mathematical Theory of Primal Sketch and Sketchability

## Speaker:

Ying Nian Wu

UCLA Department of Statistics

Time: Friday 28 March 10:15-11:00 am

Place: N014 DIKU

## Abstract

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.