Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show that a straightforward extension of an existing GAN algorithm is not applicable to point clouds, because the constraint required for discriminators is undefined for set data. We propose a two fold modification to a GAN algorithm to be able to generate point clouds (PC-GAN). First, we combine ideas from hierarchical Bayesian modeling and implicit generative models by learning a hierarchical and interpretable sampling process. A key component of our method is that we train a posterior inference network for the hidden variables. Second, PC-GAN defines a generic framework that can incorporate many existing GAN algorithms. We further propose a sandwiching objective, which results in a tighter Wasserstein distance estimate than the commonly used dual form in WGAN. We validate our claims on the ModelNet40 benchmark dataset and observe that PC- GAN trained by the sandwiching objective achieves better results on test data than existing methods. We also conduct studies on several tasks, including generalization on unseen point clouds, latent space interpolation, classification, and image to point clouds transformation, to demonstrate the versatility of the proposed PC-GAN algorithm.
We propose a GAN variant which learns to generate point clouds. Different studies have been explores, including tighter Wasserstein distance estimate,  conditional generation, generalization to unseen point clouds and image to point cloud. This paper proposes using GAN to generate 3D point cloud and introduces a sandwiching objective, averaging the upper and lower bound of Wasserstein distance between distributions. This paper proposes a new generative model for unordered data, with a particular application to point clouds, which includes an inference method and a novel objective function. 