(Just) A Spoonful of Refinements Helps the Registration Error Go Down

TL;DR

This paper introduces a refined differentiable layer for 3D point cloud registration that improves correspondence matching and reduces rotation error by linearizing constraints and iteratively updating estimates.

Contribution

It extends the Kabsch algorithm with a linearized constraint approach, enhancing learning-based registration accuracy.

Findings

Up to 7% reduction in rotation error.

Improved correspondence matching quality.

Effective integration with existing methods.

Abstract

We tackle data-driven 3D point cloud registration. Given point correspondences, the standard Kabsch algorithm provides an optimal rotation estimate. This allows to train registration models in an end-to-end manner by differentiating the SVD operation. However, given the initial rotation estimate supplied by Kabsch, we show we can improve point correspondence learning during model training by extending the original optimization problem. In particular, we linearize the governing constraints of the rotation matrix and solve the resulting linear system of equations. We then iteratively produce new solutions by updating the initial estimate. Our experiments show that, by plugging our differentiable layer to existing learning-based registration methods, we improve the correspondence matching quality. This yields up to a 7% decrease in rotation error for correspondence-based data-driven registration methods.