# Making Rotation Averaging Fast and Robust with Anisotropic Coordinate Descent

arXiv: https://arxiv.org/abs/2506.01940 · HTML: https://mlsanity.com/paper/2506.01940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [Convex Relaxations for Pose Graph Optimization with Outliers](https://mlsanity.com/paper/1801.02112/) (2018)
- [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)
- [A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints](https://mlsanity.com/paper/1506.00575/) (2015)
- [Block Coordinate Descent on Smooth Manifolds: Convergence Theory and Twenty-One Examples](https://mlsanity.com/paper/2305.14744/) (2023)
- [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)
- [On the Distribution of Minima in Intrinsic-Metric Rotation Averaging](https://mlsanity.com/paper/2003.08310/) (2020)
- [Performance Guarantees for Spectral Initialization in Rotation Averaging and Pose-Graph SLAM](https://mlsanity.com/paper/2201.03773/) (2022)
- [Certifiably Optimal Anisotropic Rotation Averaging](https://mlsanity.com/paper/2503.07353/) (2025)

## Abstract (arXiv)

Anisotropic rotation averaging has recently been explored as a natural extension of respective isotropic methods. In the anisotropic formulation, uncertainties of the estimated relative rotations -- obtained via standard two-view optimization -- are propagated to the optimization of absolute rotations. The resulting semidefinite relaxations are able to recover global minima but scale poorly with the problem size. Local methods are fast and also admit robust estimation but are sensitive to initialization. They usually employ minimum spanning trees and therefore suffer from drift accumulation and can get trapped in poor local minima. In this paper, we attempt to bridge the gap between optimality, robustness and efficiency of anisotropic rotation averaging. We analyze a family of block coordinate descent methods initially proposed to optimize the standard chordal distances, and derive a much simpler formulation and an anisotropic extension obtaining a fast general solver. We integrate this solver into the extended anisotropic large-scale robust rotation averaging pipeline. The resulting algorithm achieves state-of-the-art performance on public structure-from-motion datasets. Project page: https://ylochman.github.io/acd