Point-set Distances for Learning Representations of 3D Point Clouds

TL;DR

This paper systematically evaluates distance metrics for 3D point clouds and introduces sliced Wasserstein distance as an effective and efficient metric for learning representations, outperforming traditional methods like Chamfer discrepancy.

Contribution

The paper proposes using sliced Wasserstein distance for 3D point cloud representation learning and introduces a new algorithm to estimate it accurately, improving over existing metrics.

Findings

Sliced Wasserstein distance outperforms Chamfer discrepancy in learning efficiency.

The new estimation algorithm provides close approximations to the true sliced Wasserstein distance.

Applications include improved autoencoders, generative models, and registration tasks.

Abstract

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 sliced Wasserstein distance and its variants for learning representations of 3D point clouds. In addition, we introduce a new algorithm to estimate sliced Wasserstein distance that guarantees that the estimated value is close enough to the true one. Experiments show that the sliced Wasserstein distance and its variants allow the neural network to learn a more efficient representation compared to the Chamfer discrepancy. We demonstrate the efficiency of the sliced Wasserstein metric and its variants on several tasks in 3D computer vision including training a point cloud autoencoder, generative modeling, transfer learning, and point cloud registration.