Shocks from images: propagation of orientation elements

The extraction of figure symmetry from image contours faces a number of fundamental difficulties: object symmetries are distorted due to (i) gaps in the bounding contour of a shape due to figure-ground blending, weak contrast edges, highlights, noise, etc.; (ii) an introduction of parts and occluders, and (iii) spurious edge elements due to surface markings, texture, etc. A framework for extracting such symmetries from real images is proposed based on the propagation of contour orientation information and the detection of four types of singularities (shocks) arising from the collision of propagating elements. In this paper, we show that an additional labeling of shocks based on whether the colliding wavefronts carry true orientation information (regular vs. rarefaction waves) allows a division of shocks into three sets: regular shocks are the partial shocks of partial contours as they remain invariant to the completion of the contour; semi-degenerate and degenerate shocks depict potential parts and gaps. Finally, shocks altered due to spurious edges, occlusion, and gaps are recovered via a simulation of inter-penetrating waves generated at select shock groups which with the aid of the above shock labels leads to second and further generations of shocks