# Rotation Averaging: A Primal-Dual Method and Closed-Forms in Cycle Graphs

arXiv: https://arxiv.org/abs/2406.18564 · HTML: https://mlsanity.com/paper/2406.18564/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [NeuRoRA: Neural Robust Rotation Averaging](https://mlsanity.com/paper/1912.04485/) (2019)
- [Nonconvex phase synchronization](https://mlsanity.com/paper/1601.06114/) (2016)
- [Tightness of the maximum likelihood semidefinite relaxation for angular synchronization](https://mlsanity.com/paper/1411.3272/) (2014)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions](https://mlsanity.com/paper/1506.00746/) (2015)
- [On the Estimation Performance and Convergence Rate of the Generalized Power Method for Phase Synchronization](https://mlsanity.com/paper/1603.00211/) (2016)
- [A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints](https://mlsanity.com/paper/1506.00575/) (2015)
- [Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints](https://mlsanity.com/paper/1810.03930/) (2018)
- [Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs](https://mlsanity.com/paper/2109.08046/) (2021)
- [Performance Guarantees for Spectral Initialization in Rotation Averaging and Pose-Graph SLAM](https://mlsanity.com/paper/2201.03773/) (2022)

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

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)

## Abstract (arXiv)

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and structure-from-motion, the problem of synchronizing rotations also finds applications in visual simultaneous localization and mapping, where it is used as an initialization for iterative solvers, and camera network calibration. Nevertheless, this optimization problem is both non-convex and high-dimensional. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel primal-dual method, motivated by the widely accepted spectral initialization. Further, we characterize stationary points of rotation averaging in cycle graphs topologies and contextualize this result within spectral graph theory. We benchmark the proposed method in multiple settings and certify our solution via duality theory, achieving a significant gain in precision and performance.