  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.
