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Impressive progress in 3D shape extraction led to representations that cancapture object geometries with high fidelity. In parallel, primitive-basedmethods seek to represent objects as semantically consistent part arrangements.However, due to the simplicity of existing primitive representations, thesemethods fail to accurately reconstruct 3D shapes using a small number ofprimitives/parts. We address the trade-off between reconstruction quality andnumber of parts with Neural Parts, a novel 3D primitive representation thatdefines primitives using an Invertible Neural Network (INN) which implementshomeomorphic mappings between a sphere and the target object. The INN allows usto compute the inverse mapping of the homeomorphism, which in turn, enables theefficient computation of both the implicit surface function of a primitive andits mesh, without any additional post-processing. Our model learns to parse 3Dobjects into semantically consistent part arrangements without any part-levelsupervision. Evaluations on ShapeNet, D-FAUST and FreiHAND demonstrate that ourprimitives can capture complex geometries and thus simultaneously achievegeometrically accurate as well as interpretable reconstructions using an orderof magnitude fewer primitives than state-of-the-art shape abstraction methods.

Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks