用双旋转建模解决相对位姿估计问题，性能更优。
A Birotation Solution for Relative Pose Problems
- 通过两个旋转矩阵和基变换构建能量函数
- 在SO(3)流形上迭代优化，求解最优相对位姿
- 适用于多种视觉任务，效果优于传统方法
相对位姿估计是计算机视觉中的基础问题，已有方法通常通过分解本质矩阵或直接估计旋转与平移来求解。本文提出一种新颖的双旋转解决方案，引入三种与几何度量相关的基变换，分别定义对应的距离度量。基于这些度量设计三个能量函数，在SO(3)黎曼流形上通过迭代更新两个旋转矩阵进行最小化。最终利用能量最小对应的旋转矩阵与基变换恢复相对位姿。在多种相对位姿估计任务中进行了广泛的定量与定性评估，结果表明该方法性能优越。源代码、演示视频及数据集将在论文发表后公开于mias.group/birotation-solution。
原文摘要 · Abstract (English)
Relative pose estimation, a fundamental computer vision problem, has been extensively studied for decades. Existing methods either estimate and decompose the essential matrix or directly estimate the rotation and translation to obtain the solution. In this article, we break the mold by tackling this traditional problem with a novel birotation solution. We first introduce three basis transformations, each associated with a geometric metric to quantify the distance between the relative pose to be estimated and its corresponding basis transformation. Three energy functions, designed based on these metrics, are then minimized on the Riemannian manifold $\mathrm{SO(3)}$ by iteratively updating the two rotation matrices. The two rotation matrices and the basis transformation corresponding to the minimum energy are ultimately utilized to recover the relative pose. Extensive quantitative and qualitative evaluations across diverse relative pose estimation tasks demonstrate the superior performance of our proposed birotation solution. Source code, demo video, and datasets will be available at \href{https://mias.group/birotation-solution}{mias.group/birotation-solution} upon publication.
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