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 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 an energy for the whole point cloud. We call our model the Generative PointNet because it can be derived from the discriminative PointNet. Our 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 generators that rely on hand-crafted distance metrics, our model does not require any hand-crafted distance metric for the point cloud generation, because it synthesizes point clouds by matching observed examples in terms of statistical properties 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 interpolation. The learned point cloud representation can be useful for point cloud classification. Experiments demonstrate the advantages of the proposed generative model of point clouds.

翻译：我们提出一个非定序点数据集(如点云)的基因模型,其形式为以能源为基础的模型,使能源功能通过输入-透化-异性自下而上神经网络进行参数化。能源功能学习每个点的协调编码,然后将所有单个点特征综合成整个点云的能量。我们称我们模型为“创点网”,因为它可以从有区别的点网中衍生出来。我们的模型可以由以MCMC为基础的最大可能性学习(及其变种)来培训,而不需要GANs和VAEs等任何辅助网络的帮助。与依赖手制距离测量仪的大多数点云生成器不同的是,我们的模型并不要求点生成点云的任何手工制作的距离指标,因为它通过将观测到的能源函数定义的统计属性实例相匹配而合成点云。此外,我们可以学习一个短程的MCMC模型,作为点云重建与内插图的流式发电机,作为能源模型。所学的点云表模型对于云的基因分类是有用的。