Convex Decomposition And Efficient Shape Representation Using Deformable Convex Polytopes

Abstract: Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a parametric implicit shape model called Disjunctive Normal Shape Model (DNSM). The DNSM is formed as a union of polytopes which themselves are formed by intersections of halfspaces. The key idea is by deforming the polytopes, which naturally remain convex during the evolution, the polytopes capture convex parts without the need to compute convexity. The major contributions of this paper include a robust convex decomposition which also results in an efficient part-based shape representation, and a novel shape convexity measure. The experimental results show the potential of the proposed method.