  Learning an effective representation of 3D point clouds requires a good
metric to measure the discrepancy between two 3D point sets, which is
non-trivial due to their irregularity. Most of the previous works resort to
using the Chamfer discrepancy or Earth Mover's distance, but those metrics are
either ineffective in measuring the differences between point clouds or
computationally expensive. In this paper, we conduct a systematic study with
extensive experiments on distance metrics for 3D point clouds. From this study,
we propose to use a variant of the Wasserstein distance, named the sliced
Wasserstein distance, for learning representations of 3D point clouds.
Experiments show that the sliced Wasserstein distance allows the neural network
to learn a more efficient representation compared to the Chamfer discrepancy.
We demonstrate the efficiency of the sliced Wasserstein metric on several tasks
in 3D computer vision including training a point cloud autoencoder, generative
modeling, transfer learning, and point cloud registration.
