CvxNets: Learnable Convex Decomposition

Boyang Deng, Kyle Genova, Soroosh Yazdani, Sofien Bouaziz, Geoffrey Hinton, Andrea Tagliasacchi

Abstract:

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