提出可证明最优的各向异性旋转平均方法，提升视觉与机器人重建精度。
Certifiably Optimal Anisotropic Rotation Averaging
- 将测量不确定性显式建模为各向异性代价，改进优化目标
- 新松弛法在所有测试数据集上恢复全局最优解，精度显著提升
- 适合需要高精度姿态估计的三维重建与机器人定位任务
旋转平均是计算机视觉与机器人应用中的关键子问题。现有方法多聚焦于各向同性设置，未充分考虑测量内在不确定性。近期实证结果表明，引入各向异性框架（显式建模不确定性）可提升解的质量。然而，该场景下的全局优化仍具挑战。本文展示如何将各向异性代价融入可证明最优的旋转平均中，并揭示原有各向同性求解器在此场景下失效。我们提出更强的松弛方法，实验表明其在所有测试数据集上均能恢复全局最优解，且几乎在所有场景中实现更精确的重建。
原文摘要 · Abstract (English)
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 work 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 empirically show that it recovers global optima in all tested datasets and leads to more accurate reconstructions in almost all scenes.
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