用特殊酉矩阵重解旋转估计，提出新神经网络表示方法
Special Unitary Parameterized Estimators of Rotation
- 基于SU(2)重构瓦尔巴问题，导出四元数参数的线性约束
- 推导出可高效求解相关旋转问题的新方法
- 提出两种连续旋转表示，适合神经网络学习
本文从特殊酉矩阵视角重新审视旋转估计问题。首先利用SU(2)重述瓦尔巴问题，推导出多个解，这些解对相应四元数参数施加线性约束。随后，利用这些约束设计高效的求解相关问题的方法。最后，基于该理论基础，提出两种新型连续旋转表示，用于神经网络中的旋转学习。大量实验验证了所提方法的有效性。
原文摘要 · Abstract (English)
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.
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