Learning 3D Point Cloud Embeddings using Optimal Transport

Siddharth Katageri, Srinjay Sarkar, Charu Sharma

Keywords: Optimal Transport, 3D Point Cloud, Wasserstein Space, Contrastive Learning

TL;DR: We introduce a novel method to learn Wasserstein embeddings for 3D point clouds endowed by contrastive learning setup.

Abstract: Learning embeddings of any data largely depends on the ability of the target space to capture semantic relations. The widely used Euclidean space, where embeddings are represented as point vectors, is known to be lacking in its potential to exploit complex structures and relations. Contrary to standard Euclidean embeddings, in this work, we embed point clouds as discrete probability distributions in Wasserstein space. We build a contrastive learning setup to learn Wasserstein embeddings that can be used as a pre-training method with or without supervision for any downstream task. We show that the features captured by Wasserstein embeddings are better in preserving the point cloud geometry, including both global and local information, thus resulting in improved quality embeddings. We perform exhaustive experiments and demonstrate the effectiveness of our method for point cloud classification, transfer learning, segmentation and interpolation tasks over multiple datasets including synthetic and real-world objects in both supervised and self-supervised settings. We also compare against other existing methods and show that our method outperforms them in all downstream tasks. Additionally, our study reveals a promising interpretation of capturing critical points of point clouds that makes our proposed method self-explainable.

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