Shape abstraction through multiple optimal solutions

Abstract

Shape abstraction is an important problem facing researchers in many fields such as pattern recognition, computer vision, and industrial design. Given a set of shapes, a recently developed shape abstraction framework generates an abstracted shape through the correspondences between their features. The correspondences are obtained based on the optimal solution of a well known transportation problem. Considering the case where multiple optimal solutions exist for one problem, this paper ranks all optimal solutions based on how much they preserve the local neighborhood relations and creates the abstracted shape using the solution with the highest rank. Experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous shape abstraction technique. © 2011 Springer-Verlag.