Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic setting, where the intrinsic uncertainties in the measurements are not fully incorporated into the resulting optimization task. Recent empirical results suggest that moving to an anisotropic framework, where these uncertainties are explicitly included, can result in an improvement of solution quality. However, global optimization for rotation averaging has remained a challenge in this scenario. In this paper we show how anisotropic costs can be incorporated in certifiably optimal rotation averaging. We also demonstrate how existing solvers, designed for isotropic situations, fail in the anisotropic setting. Finally, we propose a stronger relaxation and show empirically that it is able to recover global optima in all tested datasets and leads to a more accurate reconstruction in all but one of the scenes.

翻译：旋转平均是计算机视觉和机器人应用中的关键子问题。现有多种求解该问题的方法，同时也有若干理论结果分析其难度与最优性。然而，这些方法大多聚焦于各向同性设定，未能将测量中的固有不确定性完全纳入最终优化任务。近期实证研究表明，转向各向异性框架——即显式纳入这些不确定性——能够提升求解质量。然而，在此场景下实现旋转平均的全局优化仍具挑战。本文展示了如何将各向异性代价函数融入可证明最优的旋转平均方法中。我们同时论证了现有针对各向同性场景设计的求解器在各向异性设定中的失效情况。最后，我们提出一种更强的松弛方法，并通过实验证明该方法能够在所有测试数据集中恢复全局最优解，且在除一个场景外的所有场景中实现更精确的重建。