Special Unitary Parameterized Estimators of Rotation

TL;DR

This paper introduces new methods for rotation estimation using special unitary matrices, reformulates Wahba's problem with $SU(2)$, and proposes neural network rotation representations validated by experiments.

Contribution

It presents a novel theoretical framework for rotation estimation with $SU(2)$ and introduces two continuous neural rotation representations.

Findings

Multiple solutions for Wahba's problem with linear quaternion constraints

Efficient methods for rotation-related problems based on these constraints

Experimental validation of the proposed neural rotation representations

Abstract

This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding quaternion parameters. We then explore applications of these constraints by formulating efficient methods for related problems. Finally, from this theoretical foundation, we propose two novel continuous representations for learning rotations in neural networks. Extensive experiments validate the effectiveness of the proposed methods.