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We propose a generative model of unordered point sets, such as point clouds,in the form of an energy-based model, where the energy function isparameterized by an input-permutation-invariant bottom-up neural network. Theenergy function learns a coordinate encoding of each point and then aggregatesall individual point features into an energy for the whole point cloud. We callour model the Generative PointNet because it can be derived from thediscriminative PointNet. Our model can be trained by MCMC-based maximumlikelihood learning (as well as its variants), without the help of anyassisting networks like those in GANs and VAEs. Unlike most point cloudgenerators that rely on hand-crafted distance metrics, our model does notrequire any hand-crafted distance metric for the point cloud generation,because it synthesizes point clouds by matching observed examples in terms ofstatistical properties defined by the energy function. Furthermore, we canlearn a short-run MCMC toward the energy-based model as a flow-like generatorfor point cloud reconstruction and interpolation. The learned point cloudrepresentation can be useful for point cloud classification. Experimentsdemonstrate the advantages of the proposed generative model of point clouds.

Generative PointNet: Deep Energy-Based Learning on Unordered Point Sets for 3D Generation, Reconstruction and Classification