Point-set Distances for Learning Representations of 3D Point Clouds
This work addresses the problem of effectively measuring discrepancy between 3D point sets for researchers and practitioners working with 3D point cloud representations, offering an incremental improvement over existing metrics.
This paper investigates distance metrics for 3D point clouds, proposing the use of sliced Wasserstein distance and its variants. The authors introduce a new algorithm for estimating sliced Wasserstein distance and demonstrate that it enables neural networks to learn more efficient representations compared to the Chamfer discrepancy across various 3D computer vision tasks.
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.