A New Convexity Measurement for 3D Meshes

Abstract

This paper presents a novel convexity measurement for 3D meshes. The new convexity measure is calculated by minimizing the ratio of the summed area of valid regions in a mesh's six views, which are projected on faces of the bounding box whose edges are parallel to the coordinate axes, to the sum of three orthogonal projected areas of the mesh. The complete definition, theoretical analysis, and a computing algorithm of our convexity measure are explicitly described. This paper also proposes a new 3D shape descriptor CD (i.e., Convexity Distribution) based on the distribution of above-mentioned ratios, which are computed by randomly rotating the mesh around its center, to better describe the object's convexity-related properties compared to existing convexity measurements. Our experiments not only show that the proposed convexity measure corresponds well with human intuition, but also demonstrate the effectiveness of the new convexity measure and the new shape descriptor by significantly improving the performance of other methods in the application of 3D shape retrieval.