# Robust Single Rotation Averaging

arXiv: https://arxiv.org/abs/2004.00732 · HTML: https://mlsanity.com/paper/2004.00732/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 12 of 12)

- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [Practical, Fast and Robust Point Cloud Registration for 3D Scene Stitching and Object Localization](https://mlsanity.com/paper/2111.04228/) (2021)
- [Kernel-Based Generalized Median Computation for Consensus Learning](https://mlsanity.com/paper/2209.10208/) (2022)
- [PCR-99: A Practical Method for Point Cloud Registration with 99 Percent Outliers](https://mlsanity.com/paper/2402.16598/) (2024)
- [Incremental Multiview Point Cloud Registration with Two-stage Candidate Retrieval](https://mlsanity.com/paper/2407.07525/) (2024)
- [MV-ROPE: Multi-view Constraints for Robust Category-level Object Pose and Size Estimation](https://mlsanity.com/paper/2308.08856/) (2023)
- [Quantum Multiple Rotation Averaging](https://mlsanity.com/paper/2602.10115/) (2026)
- [Outlier-Robust Geometric Perception: A Novel Thresholding-Based Estimator with Intra-Class Variance Maximization](https://mlsanity.com/paper/2204.01324/) (2022)

## Abstract (arXiv)

We propose a novel method for single rotation averaging using the Weiszfeld algorithm. Our contribution is threefold: First, we propose a robust initialization based on the elementwise median of the input rotation matrices. Our initial solution is more accurate and robust than the commonly used chordal L2-mean. Second, we propose an outlier rejection scheme that can be incorporated in the Weiszfeld algorithm to improve the robustness of L1 rotation averaging. Third, we propose a method for approximating the chordal L1-mean using the Weiszfeld algorithm. An extensive evaluation shows that both our method and the state of the art perform equally well with the proposed outlier rejection scheme, but ours is 2-4 times faster.