# Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n

arXiv: https://arxiv.org/abs/2008.02737 · HTML: https://mlsanity.com/paper/2008.02737/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2020.

## Built on by (most cited first, 30 of 46)

- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [LU-NeRF: Scene and Pose Estimation by Synchronizing Local Unposed NeRFs](https://mlsanity.com/paper/2306.05410/) (2023)
- [Jigsaw: Learning to Assemble Multiple Fractured Objects](https://mlsanity.com/paper/2305.17975/) (2023)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [Revisiting Rotation Averaging: Uncertainties and Robust Losses](https://mlsanity.com/paper/2303.05195/) (2023)
- [Advances in Inference and Representation for Simultaneous Localization and Mapping](https://mlsanity.com/paper/2103.05041/) (2021)
- [Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging](https://mlsanity.com/paper/2103.08292/) (2021)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs](https://mlsanity.com/paper/2109.08046/) (2021)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation](https://mlsanity.com/paper/2407.13537/) (2024)
- [RAGO: Recurrent Graph Optimizer For Multiple Rotation Averaging](https://mlsanity.com/paper/2212.07211/) (2022)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [3D Geometric Shape Assembly via Efficient Point Cloud Matching](https://mlsanity.com/paper/2407.10542/) (2024)
- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
- [Distributed Global Structure-from-Motion with a Deep Front-End](https://mlsanity.com/paper/2311.18801/) (2023)
- [Building Rome with Convex Optimization](https://mlsanity.com/paper/2502.04640/) (2025)
- [On the Tightness of Semidefinite Relaxations for Rotation Estimation](https://mlsanity.com/paper/2101.02099/) (2021)
- [Rotation Synchronization via Deep Matrix Factorization](https://mlsanity.com/paper/2305.05268/) (2023)
- [An Overview of the Burer-Monteiro Method for Certifiable Robot Perception](https://mlsanity.com/paper/2410.00117/) (2024)
- [Orthogonal Group Synchronization with Incomplete Measurements: Error Bounds and Linear Convergence of the Generalized Power Method](https://mlsanity.com/paper/2112.06556/) (2021)
- [RL-PGO: Reinforcement Learning-based Planar Pose-Graph Optimization](https://mlsanity.com/paper/2202.13221/) (2022)
- [From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation](https://mlsanity.com/paper/2312.05995/) (2023)
- [Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization](https://mlsanity.com/paper/2407.04260/) (2024)
- [Towards Initialization-free Calibrated Bundle Adjustment](https://mlsanity.com/paper/2506.23808/) (2025)
- [Accelerating Certifiable Estimation with Preconditioned Eigensolvers](https://mlsanity.com/paper/2207.05257/) (2022)
- [Gravity-aligned Rotation Averaging with Circular Regression](https://mlsanity.com/paper/2410.12763/) (2024)
- [Combinative Matching for Geometric Shape Assembly](https://mlsanity.com/paper/2508.09780/) (2025)
- [HOSt3R: Keypoint-free Hand-Object 3D Reconstruction from RGB images](https://mlsanity.com/paper/2508.16465/) (2025)

## Abstract (arXiv)

Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.