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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 in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. 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. However, at testing time, convexes can also generate explicit representations -- polygonal meshes -- which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology, yet preserve
Decomposing a scene into its shape, reflectance, and illumination is a challenging but important problem in computer vision and graphics. This problem is inherently more challenging when the illumination is not a single light source under laboratory
The problems of shape classification and part segmentation from 3D point clouds have garnered increasing attention in the last few years. Both of these problems, however, suffer from relatively small training sets, creating the need for statistically
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we propose a nove
With the increased deployment of face recognition systems in our daily lives, face presentation attack detection (PAD) is attracting a lot of attention and playing a key role in securing face recognition systems. Despite the great performance achieve