  This paper addresses the problem of unsupervised parts-aware point cloud
generation with learned parts-based self-similarity. Our SPA-VAE infers a set
of latent canonical candidate shapes for any given object, along with a set of
rigid body transformations for each such candidate shape to one or more
locations within the assembled object. In this way, noisy samples on the
surface of, say, each leg of a table, are effectively combined to estimate a
single leg prototype. When parts-based self-similarity exists in the raw data,
sharing data among parts in this way confers numerous advantages: modeling
accuracy, appropriately self-similar generative outputs, precise in-filling of
occlusions, and model parsimony. SPA-VAE is trained end-to-end using a
variational Bayesian approach which uses the Gumbel-softmax trick for the
shared part assignments, along with various novel losses to provide appropriate
inductive biases. Quantitative and qualitative analyses on ShapeNet demonstrate
the advantage of SPA-VAE.
