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.

翻译：本文提出了一种新颖的鲁棒单旋转平均方法，可高效处理极高比例的外点。该方法旨在最小化测地距离的总截断最小非平方偏差（TLUD）代价。所提算法包含三个步骤：首先，将每个输入旋转视为潜在初始解，选择使得截断弦偏差之和最小的初始解；其次，利用该初始解获取内点集并计算其弦$L_2$均值；最后，以此估计值为起点，在$SO(3)$上运用Weiszfeld算法迭代计算内点的测地$L_1$均值。广泛评估表明，在足够数量精确内点条件下，该方法可鲁棒应对高达99%的外点，性能超越当前最优技术。