# Certifiably Optimal Anisotropic Rotation Averaging

arXiv: https://arxiv.org/abs/2503.07353 · HTML: https://mlsanity.com/paper/2503.07353/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Synchronizing Probability Measures on Rotations via Optimal Transport](https://mlsanity.com/paper/2004.00663/) (2020)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions](https://mlsanity.com/paper/1506.00746/) (2015)
- [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)
- [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)
- [Robust Group Synchronization via Quadratic Programming](https://mlsanity.com/paper/2206.08994/) (2022)
- [On the Distribution of Minima in Intrinsic-Metric Rotation Averaging](https://mlsanity.com/paper/2003.08310/) (2020)
- [Semidefinite descriptions of the convex hull of rotation matrices](https://mlsanity.com/paper/1403.4914/) (2014)
- [Visual SLAM: Why Bundle Adjust?](https://mlsanity.com/paper/1902.03747/) (2019)
- [Certifiably Optimal Rotation and Pose Estimation Based on the Cayley Map](https://mlsanity.com/paper/2308.12418/) (2023)
- [On Semidefinite Relaxations for Matrix-Weighted State-Estimation Problems in Robotics](https://mlsanity.com/paper/2308.07275/) (2023)
- [Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation](https://mlsanity.com/paper/1401.3700/) (2014)

## Built on by (most cited first, 2 of 2)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Making Rotation Averaging Fast and Robust with Anisotropic Coordinate Descent](https://mlsanity.com/paper/2506.01940/) (2025)

## Abstract (arXiv)

Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic setting, where the intrinsic uncertainties in the measurements are not fully incorporated into the resulting optimization task. Recent empirical results suggest that moving to an anisotropic framework, where these uncertainties are explicitly included, can result in an improvement of solution quality. However, global optimization for rotation averaging has remained a challenge in this scenario. In this work we show how anisotropic costs can be incorporated in certifiably optimal rotation averaging. We also demonstrate how existing solvers, designed for isotropic situations, fail in the anisotropic setting. Finally, we propose a stronger relaxation and empirically show that it recovers global optima in all tested datasets and leads to more accurate reconstructions in almost all scenes.