Convexity-based method for extracting object parts from 3-D surfaces

We describe a new method for shape decomposition which relies exclusively on global properties of the surface which are fully characterized by local surface properties. We propose that a useful parcellation of shapes into parts can be obtained by decomposing the shape boundary into the largest convex surface patches (LCP) and the smallest nonconvex surface patches. The essential computational steps of this method are the following (i) build initial parts from the largest locally convex patches, (ii) consider an initial part as a constituent pat if it is essentially convex, and (iii) obtain the remaining constituent parts by merging adjacent initial parts generated by the largest locally convex and the smallest convex patches of nearly the same sizes. We show that the decomposition of shapes into the largest convex patchesaims to maximize the 'thingness' in an object, and to minimize its 'non-thingness', that is the method is conductive to a natural parcellation of shapes into constituent parts useful for recognition and for inferring function.