Abstract

Given a set of points corresponding to a 2D projection of a non-planar shape, we would like to obtain a representation invariant to articulations (under no self-occlusions). It is a chal lenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint variations, as wel l as the varying effects of imaging process on different regions of the shape due to its non-planarity. By modeling an articulating shape as a combination of approximate convex parts con- nected by non-convex junctions, we propose to preserve distances between a pair of points by (i) estimating the parts of the shape through approxi- mate convex decomposition, by introducing a robust measure of convexity and (ii) performing part-wise affine normalization by assuming a weak perspective camera model, and then relating the points using the inner distance which is insensitive to planar articulations. We demonstrate the effectiveness of our representation on a dataset with non-planar ar- ticulations, and on standard shape retrieval datasets like MPEG-7.