Title: Special Unitary Parameterized Estimators of Rotation
Primary area: optimization
Keywords: optimization, special unitary, rotation estimation, quaternion, learning rotations, machine learning, Wahba's Problem

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.

TL;DR: Solving Wahba's problem with special unitary matrices, leading to new optimization formulations as well as representations for learning rotations in neural networks.