Abstract
Organizing shape representations in terms of parts allows one to separate the representation of individual parts from the representation of their spatial relationships—thereby providing a robust representation of shape that is stable across changes in the articulated pose of an object. However, the general problem of how the visual system segments shapes into parts remains unsolved. An attractive possibility, going back to the work of Blum (1973), is to compute parts based on the axial branches in a skeleton-based description of the shape—in other words, to isomorphize axes and parts. This approach fails, however, because of the numerous spurious axes produced by the Medial Axis Transform and its modern descendants. Most notable of these problems are the forking of the axes at the ends of blunt parts, and the extreme sensitivity to contour noise. In previous work, we proposed a Bayesian approach to the estimation of a shape's skeleton that overcomes these problems (Feldman & Singh, PNAS 2006). Our approach treats shapes as arising from a mixture of generative factors and noise, and the maximum-a-posteriori (MAP) skeleton (the skeletal structure most likely to have generated a given shape) provides a perceptually reasonable estimate of the shape's skeleton. Here we show that the MAP skeleton also provides a perceptually natural account of part decomposition. Known geometric determinants of part decomposition and part salience—including negative minima of curvature, cut length, curvature, protrusion, necks and limbs—all naturally fall out of the Bayesian skeleton estimation. Specifically, the influence of these geometric variables on part segmentation/salience is reflected in the posterior probabilities associated with the corresponding MAP skeletons—despite the fact that our scheme does not explicitly compute contour curvature. This allows the part segmentation problem to be grounded in a single unifying process of Bayesian estimation of the shape skeleton.
NSF DGE 0549115 (Rutgers IGERT in Perceptual Science) NSF BCS-0216944 NIH R01 EY15888.