Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning

TL;DR

This paper presents a novel unsupervised SE(3) point cloud registration method that operates without correspondences, using RKHS and equivariant features to achieve high accuracy on synthetic and real datasets, including RGB-D odometry.

Contribution

It introduces a correspondence-free, unsupervised registration approach leveraging RKHS and SE(3)-equivariant features, with a new distance metric for robust performance.

Findings

Outperforms classical and supervised methods in accuracy.

Effective on synthetic and real noisy datasets.

First to register real RGB-D odometry data with an equivariant method.

Abstract

This paper introduces a robust unsupervised SE(3) point cloud registration method that operates without requiring point correspondences. The method frames point clouds as functions in a reproducing kernel Hilbert space (RKHS), leveraging SE(3)-equivariant features for direct feature space registration. A novel RKHS distance metric is proposed, offering reliable performance amidst noise, outliers, and asymmetrical data. An unsupervised training approach is introduced to effectively handle limited ground truth data, facilitating adaptation to real datasets. The proposed method outperforms classical and supervised methods in terms of registration accuracy on both synthetic (ModelNet40) and real-world (ETH3D) noisy, outlier-rich datasets. To our best knowledge, this marks the first instance of successful real RGB-D odometry data registration using an equivariant method. The code is available at {https://sites.google.com/view/eccv24-equivalign}