  Impressive progress in 3D shape extraction led to representations that can
capture object geometries with high fidelity. In parallel, primitive-based
methods seek to represent objects as semantically consistent part arrangements.
However, due to the simplicity of existing primitive representations, these
methods fail to accurately reconstruct 3D shapes using a small number of
primitives/parts. We address the trade-off between reconstruction quality and
number of parts with Neural Parts, a novel 3D primitive representation that
defines primitives using an Invertible Neural Network (INN) which implements
homeomorphic mappings between a sphere and the target object. The INN allows us
to compute the inverse mapping of the homeomorphism, which in turn, enables the
efficient computation of both the implicit surface function of a primitive and
its mesh, without any additional post-processing. Our model learns to parse 3D
objects into semantically consistent part arrangements without any part-level
supervision. Evaluations on ShapeNet, D-FAUST and FreiHAND demonstrate that our
primitives can capture complex geometries and thus simultaneously achieve
geometrically accurate as well as interpretable reconstructions using an order
of magnitude fewer primitives than state-of-the-art shape abstraction methods.
