# Correspondence-Free Fast and Robust Spherical Point Pattern Registration

arXiv: https://arxiv.org/abs/2508.02339 · HTML: https://mlsanity.com/paper/2508.02339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 82 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 27 of 27)

- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [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)
- [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)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [PCRNet: Point Cloud Registration Network using PointNet Encoding](https://mlsanity.com/paper/1908.07906/) (2019)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [Learning general and distinctive 3D local deep descriptors for point cloud registration](https://mlsanity.com/paper/2105.10382/) (2021)
- [ROBIN: a Graph-Theoretic Approach to Reject Outliers in Robust Estimation using Invariants](https://mlsanity.com/paper/2011.03659/) (2020)
- [Star Tracking using an Event Camera](https://mlsanity.com/paper/1812.02895/) (2018)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [ReAgent: Point Cloud Registration using Imitation and Reinforcement Learning](https://mlsanity.com/paper/2103.15231/) (2021)
- [GOGMA: Globally-Optimal Gaussian Mixture Alignment](https://mlsanity.com/paper/1603.00150/) (2016)
- [Scaling Spherical CNNs](https://mlsanity.com/paper/2306.05420/) (2023)
- [A Practical Maximum Clique Algorithm for Matching with Pairwise Constraints](https://mlsanity.com/paper/1902.01534/) (2019)
- [RANSIC: Fast and Highly Robust Estimation for Rotation Search and Point Cloud Registration using Invariant Compatibility](https://mlsanity.com/paper/2104.09133/) (2021)
- [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)
- [Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Training](https://mlsanity.com/paper/2206.11215/) (2022)
- [Efficient Global Point Cloud Alignment using Bayesian Nonparametric Mixtures](https://mlsanity.com/paper/1603.04868/) (2016)
- [Semidefinite descriptions of the convex hull of rotation matrices](https://mlsanity.com/paper/1403.4914/) (2014)

## Built on by (most cited first, 1 of 1)

- [Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment](https://mlsanity.com/paper/2512.00659/) (2025)

## Abstract (arXiv)

Existing methods for rotation estimation between two spherical (mathbbS2) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities greater than cubic O(n3) with respect to rotation space discretization and lack extensive evaluation under significant outlier contamination. To this end, we propose a rotation estimation algorithm between two spherical patterns with linear time complexity O(n). Unlike existing spherical-function-based methods, we explicitly represent spherical patterns as discrete 3D point sets on the unit sphere, reformulating rotation estimation as a spherical point-set alignment (i.e., Wahba problem for 3D unit vectors). Given the geometric nature of our formulation, our spherical pattern alignment algorithm naturally aligns with the Wahba problem framework for 3D unit vectors. Specifically, we introduce three novel algorithms: (1) SPMC (Spherical Pattern Matching by Correlation), (2) FRS (Fast Rotation Search), and (3) a hybrid approach (SPMC+FRS) that combines the advantages of the previous two methods. Our experiments demonstrate that in the mathbbS2 domain and in correspondence-free settings, our algorithms are over 10x faster and over 10x more accurate than current state-of-the-art methods for the Wahba problem with outliers. We validate our approach through extensive simulations on a new dataset of spherical patterns, the ``Robust Vector Alignment Dataset. "Furthermore, we adapt our methods to two real-world tasks: (i) Point Cloud Registration (PCR) and (ii) rotation estimation for spherical images.