# Accelerating Outlier-robust Rotation Estimation by Stereographic Projection

arXiv: https://arxiv.org/abs/2502.06337 · HTML: https://mlsanity.com/paper/2502.06337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (2022)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus](https://mlsanity.com/paper/2001.02643/) (2020)
- [PHASER: a Robust and Correspondence-free Global Pointcloud Registration](https://mlsanity.com/paper/2102.02767/) (2021)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [DetarNet: Decoupling Translation and Rotation by Siamese Network for Point Cloud Registration](https://mlsanity.com/paper/2112.14059/) (2021)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [On the Tightness of Semidefinite Relaxations for Rotation Estimation](https://mlsanity.com/paper/2101.02099/) (2021)
- [Multi-Model 3D Registration: Finding Multiple Moving Objects in Cluttered Point Clouds](https://mlsanity.com/paper/2402.10865/) (2024)
- [Speeding Up Iterative Closest Point Using Stochastic Gradient Descent](https://mlsanity.com/paper/1907.09133/) (2019)
- [ROSIA: Rotation-Search-Based Star Identification Algorithm](https://mlsanity.com/paper/2210.00429/) (2022)

## Abstract (arXiv)

Rotation estimation plays a fundamental role in many computer vision and robot tasks. However, efficiently estimating rotation in large inputs containing numerous outliers (i.e., mismatches) and noise is a recognized challenge. Many robust rotation estimation methods have been designed to address this challenge. Unfortunately, existing methods are often inapplicable due to their long computation time and the risk of local optima. In this paper, we propose an efficient and robust rotation estimation method. Specifically, our method first investigates geometric constraints involving only the rotation axis. Then, it uses stereographic projection and spatial voting techniques to identify the rotation axis and angle. Furthermore, our method efficiently obtains the optimal rotation estimation and can estimate multiple rotations simultaneously. To verify the feasibility of our method, we conduct comparative experiments using both synthetic and real-world data. The results show that, with GPU assistance, our method can solve large-scale (106 points) and severely corrupted (90% outlier rate) rotation estimation problems within 0.07 seconds, with an angular error of only 0.01 degrees, which is superior to existing methods in terms of accuracy and efficiency.