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A Bayesian Approach to Shape

Dr. Jacob Feldman

Monday, October 16, 2006, 01:00pm - 02:00pm

Rutgers University, Department of Psychology and the Center for Cognitive Science

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The mental representation of shape, a critical problem in visual perception, is still surprisingly poorly understood. For example it is widely accepted that a critical part of shape representation is the division of a shape into component parts, but the computational rules by which the visual system accomplishes this are somewhat complicated and heterogeneous, and lack a principled theory. The subjective decomposition of a shape into parts can't be explained by any simple local rule: it respects global shape organization in a number of subtle ways that current theories cannot adequately handle. The key to the resolution of these problems is the robust estimation of a shape's skeleton---a notoriously difficult problem.

In this talk I'll present a new Bayesian framework (developed jointly with Manish Singh) for estimating the shape skeleton, which solves many of the standard difficulties. In the Bayesian approach, we adopt a prior over shape skeletons (which penalizes complex or branching skeletons), and a generative (likelihood) model of shape in which contours are generated from skeletons with approximately perpendicular "ribs" exhibiting some random error. With the prior and likelihood models in hand, we can estimate the shape skeleton that maximizes the posterior, called the MAP skeleton, which is the skeletal hypothesis that best "explains" the observed shape. I'll show examples suggesting that this method gives more intuitive results than traditional medial axis methods. Generally, each axis in the MAP skeleton corresponds to an intuitive part of the shape, making it suitable as a basis for psychological shape representation and part decomposition.

Dr. Jacob Feldman