We propose a generative model of unordered point sets, such as point clouds, in the forms of an energy-based model, where the energy function is parameterized by an input-permutation-invariant bottom-up neural network. The energy function learns a coordinate encoding of each point and then aggregates all individual point features into energy for the whole point cloud. We show that our model can be derived from the discriminative PointNet. The model can be trained by MCMC-based maximum likelihood learning (as well as its variants), without the help of any assisting networks like those in GANs and VAEs. Unlike most point cloud generator that relys on hand-crafting distance metrics, our model does not rely on hand-crafting distance metric for point cloud generation, because it synthesizes point clouds by matching observed examples in terms of statistical property defined by the energy function. Furthermore, we can learn a short-run MCMC toward the energy-based model as a flow-like generator for point cloud reconstruction and interpretation. The learned point cloud representation can be also useful for point cloud classification. Experiments demonstrate the advantages of the proposed generative model of point clouds.

本研究提出了一种基于能量的无序点集生成模型，通过MCMC最大似然学习来训练模型，并且不需要手工定义距离的度量标准来产生点云。该模型可以用于点云分类和插值。

Generative PointNet：基于深度能量的无序点集学习，用于3D生成，重建和分类