A New Volume-Based Convexity Measure for 3D Shapes

Convexity, as a global and learning-free shape descriptor, has been widely applied to shape classification, retrieval and decomposition. Unlike its extensively addressed 2D counterpart, 3D shape convexity measurement attracting insufficient attention has yet to be studied. In this paper, we put forward a new volume-based convexity measure for 3D shapes, which builds on a conventional volume-based convexity measure but excels it by resolving its problems. By turning the convexity measurement into a problem of influence evaluation through Distance-weighted Volume Integration, the new convexity measure can resolve the major problems of the existing ones and accelerate the overall computational time.