Robust Point Cloud Processing through Positional Embedding

TL;DR

This paper introduces a robust point cloud processing method using analytical positional embeddings based on bandwidth, improving resilience to out-of-distribution noise and outliers in tasks like classification and registration.

Contribution

It proposes a novel analytical per-point embedding based on bandwidth, connecting it to positional embeddings like random Fourier features for enhanced robustness.

Findings

Improved robustness to OOD noise in point cloud tasks

Enhanced performance in classification and registration

Connections established between bandwidth-based and positional embeddings

Abstract

End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants -- all employ learned per-point embeddings. Despite impressive performance, such approaches are sensitive to out-of-distribution (OOD) noise and outliers. In this paper, we explore the role of an analytical per-point embedding based on the criterion of bandwidth. The concept of bandwidth enables us to draw connections with an alternate per-point embedding -- positional embedding, particularly random Fourier features. We present compelling robust results across downstream tasks such as point cloud classification and registration with several categories of OOD noise.