In this work, we propose a novel method for robust single rotation averaging
that can efficiently handle an extremely large fraction of outliers. Our
approach is to minimize the total truncated least unsquared deviations (TLUD)
cost of geodesic distances. The proposed algorithm consists of three steps:
First, we consider each input rotation as a potential initial solution and
choose the one that yields the least sum of truncated chordal deviations. Next,
we obtain the inlier set using the initial solution and compute its chordal
$L_2$-mean. Finally, starting from this estimate, we iteratively compute the
geodesic $L_1$-mean of the inliers using the Weiszfeld algorithm on $SO(3)$. An
extensive evaluation shows that our method is robust against up to 99% outliers
given a sufficient number of accurate inliers, outperforming the current state
of the art.

基于最小化截断的欧氏距离的平均旋转方法，具有较强的抗干扰性能，优于当前领先的方法。

稳健的单次旋转平均重新审视

Robust Single Rotation Averaging Revisited

We propose a novel method for single rotation averaging using the Weiszfeld
algorithm. Our contribution is threefold: First, we propose a robust
initialization based on the elementwise median of the input rotation matrices.
Our initial solution is more accurate and robust than the commonly used chordal
$L_2$-mean. Second, we propose an outlier rejection scheme that can be
incorporated in the Weiszfeld algorithm to improve the robustness of $L_1$
rotation averaging. Third, we propose a method for approximating the chordal
$L_1$-mean using the Weiszfeld algorithm. An extensive evaluation shows that
both our method and the state of the art perform equally well with the proposed
outlier rejection scheme, but ours is $2-4$ times faster.

本研究提出了一种利用 Weiszfeld 算法进行单旋转平均的新方法，其三个亮点是鲁棒初始化、离群值剔除和利用 Weiszfeld 算法近似计算 chordal L1-mean。全面的评估表明，我们的方法和现有技术在采用所提离群值剔除方案时表现相似，但速度快 2-4 倍。