# Robust Single Rotation Averaging Revisited

arXiv: https://arxiv.org/abs/2309.05388 · HTML: https://mlsanity.com/paper/2309.05388/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [On-Manifold Preintegration for Real-Time Visual-Inertial Odometry](https://mlsanity.com/paper/1512.02363/) (2015)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [Loc-NeRF: Monte Carlo Localization using Neural Radiance Fields](https://mlsanity.com/paper/2209.09050/) (2022)
- [ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants](https://mlsanity.com/paper/2011.03659/) (2020)
- [Object Pose Estimation with Statistical Guarantees: Conformal Keypoint Detection and Geometric Uncertainty Propagation](https://mlsanity.com/paper/2303.12246/) (2023)
- [Modeling Perceptual Aliasing in SLAM via Discrete-Continuous Graphical Models](https://mlsanity.com/paper/1810.11692/) (2018)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers](https://mlsanity.com/paper/2006.06769/) (2020)
- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [Robust Single Rotation Averaging](https://mlsanity.com/paper/2004.00732/) (2020)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [Practical, Fast and Robust Point Cloud Registration for 3D Scene Stitching and Object Localization](https://mlsanity.com/paper/2111.04228/) (2021)

## Built on by (most cited first, 6 of 6)

- [Alignment Scores: Robust Metrics for Multiview Pose Accuracy Evaluation](https://mlsanity.com/paper/2407.20391/) (2024)
- [PCR-99: A Practical Method for Point Cloud Registration with 99 Percent Outliers](https://mlsanity.com/paper/2402.16598/) (2024)
- [Robustness of Generalized Median Computation for Consensus Learning in Arbitrary Spaces](https://mlsanity.com/paper/2503.05215/) (2025)
- [Quantum Multiple Rotation Averaging](https://mlsanity.com/paper/2602.10115/) (2026)
- [SNAP: A Self-Consistent Agreement Principle with Application to Robust Computation](https://mlsanity.com/paper/2602.02013/) (2026)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)

## Abstract (arXiv)

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 L2-mean. Finally, starting from this estimate, we iteratively compute the geodesic L1-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.