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：本文提出了一种鲁棒单旋转均值的新方法，能够高效处理极高比例的外点。我们的方法是最小化测地距离的截断最小化未平方偏差（TLUD）总代价。所提算法包含三个步骤：首先，将每个输入旋转作为潜在初始解，选取使截断弦偏离总和最小的解；其次，利用初始解获取内点集并计算其弦$L_2$均值；最后，从该估计值出发，通过$SO(3)$上的Weiszfeld算法迭代计算内点的测地$L_1$均值。大量评估表明，当存在足够数量的精确内点时，本方法对高达99%的外点具有鲁棒性，性能优于当前最先进方法。