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.
We investigate the problem of learning category-specific 3D surface shape reconstruction from a variable number of RGB views of previously unobserved object instances. Most approaches for multiview shape reconstruction operate on sparse shape representations, or assume a fixed number of views. We present a method that can estimate dense 3D shape, and aggregate shape across multiple and varying number of input views. Given a single input view of an object instance, we propose a representation that encodes the dense shape of the visible object surface parts as well as the surface behind line of sight and occluded by the visible surface. When multiple input views are available, the shape representation is designed to be aggregated into a single 3D shape using an inexpesive union operation. We train a 2D CNN to learn to predict this representation from a variable number of views (1 or more). We further aggregate multiview information by using permutation equivariant layers that promote order-agnostic view information exchange at the feature level. Experiments show that our approach is able to produce dense reconstructions of objects, and is able to produce better results as more views are added.