CvxNets: Learnable Convex Decomposition

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental to real-time physics simulation in computer graphics, where it creates a unifying representation of dynamic geometry for collision detection. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an autoencoding process. We investigate the applications of the network including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.