# Linearly Solving Robust Rotation Estimation

arXiv: https://arxiv.org/abs/2506.11547 · HTML: https://mlsanity.com/paper/2506.11547/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 118 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 30 of 31)

- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [Event-Based Motion Segmentation by Motion Compensation](https://mlsanity.com/paper/1904.01293/) (2019)
- [Efficient Algorithms for Outlier-Robust Regression](https://mlsanity.com/paper/1803.03241/) (2018)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [Deep Hough Transform for Semantic Line Detection](https://mlsanity.com/paper/2003.04676/) (2020)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [EM Converges for a Mixture of Many Linear Regressions](https://mlsanity.com/paper/1905.12106/) (2019)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [A Practical Maximum Clique Algorithm for Matching with Pairwise Constraints](https://mlsanity.com/paper/1902.01534/) (2019)
- [Convex Relaxations for Pose Graph Optimization with Outliers](https://mlsanity.com/paper/1801.02112/) (2018)
- [Practical optimal registration of terrestrial LiDAR scan pairs](https://mlsanity.com/paper/1811.09962/) (2018)
- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [A New Outlier Removal Strategy Based on Reliability of Correspondence Graph for Fast Point Cloud Registration](https://mlsanity.com/paper/2205.07404/) (2022)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Multi-Model 3D Registration: Finding Multiple Moving Objects in Cluttered Point Clouds](https://mlsanity.com/paper/2402.10865/) (2024)
- [Certifiably Optimal Rotation and Pose Estimation Based on the Cayley Map](https://mlsanity.com/paper/2308.12418/) (2023)
- [Accurate Peak Detection in Multimodal Optimization via Approximated Landscape Learning](https://mlsanity.com/paper/2503.18066/) (2025)
- [ANSAC: Adaptive Non-minimal Sample and Consensus](https://mlsanity.com/paper/1709.09559/) (2017)
- [Fast and Globally Optimal Rigid Registration of 3D Point Sets by Transformation Decomposition](https://mlsanity.com/paper/1812.11307/) (2018)
- [General techniques for approximate incidences and their application to the camera posing problem](https://mlsanity.com/paper/1903.07047/) (2019)
- [Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior](https://mlsanity.com/paper/2311.01432/) (2023)
- [Efficient Large Scale Inlier Voting for Geometric Vision Problems](https://mlsanity.com/paper/2107.11810/) (2021)

## Abstract (arXiv)

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear and non-convex optimization problem that requires careful design. However, in this paper, we provide some new perspectives that solving a rotation estimation problem can be reformulated as solving a linear model fitting problem without dropping any constraints and without introducing any singularities. In addition, we explore the dual structure of a rotation motion, revealing that it can be represented as a great circle on a quaternion sphere surface. Accordingly, we propose an easily understandable voting-based method to solve rotation estimation. The proposed method exhibits exceptional robustness to noise and outliers and can be computed in parallel with graphics processing units (GPUs) effortlessly. Particularly, leveraging the power of GPUs, the proposed method can obtain a satisfactory rotation solution for large-scale(106) and severely corrupted (99% outlier ratio) rotation estimation problems under 0.5 seconds. Furthermore, to validate our theoretical framework and demonstrate the superiority of our proposed method, we conduct controlled experiments and real-world dataset experiments. These experiments provide compelling evidence supporting the effectiveness and robustness of our approach in solving rotation estimation problems.