A heuristic convexity measure for 3D meshes

In this paper we propose a heuristic convexity measure for 3D meshes. Built upon a state-of-the-art convexity measure that employs a time-consuming genetic algorithm for optimization, our new measure projects only once a given 3D mesh onto the orthogonal 2D planes along its principal directions for an initial estimation of mesh convexity, followed by a correction calculation based on mesh slicing. Our measure experimentally shows several advantages over the state-of-the-art one: first, it accelerates the overall computation by approximately an order of magnitude; second, it properly handles those bony meshes usually overestimated by the state-of-the-art measure; third, it improves the accuracy of the state-of-the-art measure in 3D mesh retrieval.