Robust Single Rotation Averaging Revisited

TL;DR

The paper introduces a robust single rotation averaging method that handles extreme outlier fractions by minimizing the total TLUD cost on $SO(3)$. A simple yet effective initialization tests every input rotation using a chordal-distance proxy to identify a reliable inlier set, followed by refining the rotation via the geodesic $L_1$-mean with the Weiszfeld algorithm. Empirical results show state-of-the-art robustness up to $99\%$ outliers and favorable speed compared to baselines, including in point-cloud registration tasks. The approach combines a fast proxy-based initialization with a principled robust aggregation step, offering practical impact for robotics and vision systems dealing with大量 outlier contamination.

Abstract

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.

Figures (8)

• Figure 1: The TLS yang_2020_ral and the TLUD cost \ref{['eq:TLUD']}. In this work, we formulate the single rotation averaging problem as minimization of the total TLUD cost under the geodesic metric.
• Figure 2: Synopsis of the single rotation averaging problem. The unknown rotation can be estimated by averaging multiple noisy (and possibly outlier-contaminated) estimates of it.
• Figure 3: $\bm{[\sigma=5^\circ]}$ Comparison of the average rotation errors when the inlier noise level of the simulated input rotations is 5 deg (1000 Monte Carlo runs). The accuracy of our method is comparable to that of Lee2020 robust_single_rotation_averaging when the outlier ratio is low. However, our method is much more robust when the outlier ratio is high.
• Figure 4: $\bm{[\sigma=15^\circ]}$ Comparison of the average rotation errors when the inlier noise level of the simulated input rotations is 15 deg (1000 Monte Carlo runs). The accuracy of our method is comparable to that of Lee2020 robust_single_rotation_averaging when the outlier ratio is low. However, our method is much more robust when the outlier ratio is high.
• Figure 5: Rotation errors when averaging 1000 rotations with inlier noise level of 5 deg (1000 Monte-Carlo runs). Among the three methods, only ours can handle up to 99% outliers.