# Dual Quaternion SE(3) Synchronization with Recovery Guarantees

arXiv: https://arxiv.org/abs/2602.00324 · HTML: https://mlsanity.com/paper/2602.00324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## 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)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [Nonconvex phase synchronization](https://mlsanity.com/paper/1601.06114/) (2016)
- [Global registration of multiple point clouds using semidefinite programming](https://mlsanity.com/paper/1306.5226/) (2013)
- [On the Estimation Performance and Convergence Rate of the Generalized Power Method for Phase Synchronization](https://mlsanity.com/paper/1603.00211/) (2016)
- [A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group](https://mlsanity.com/paper/2009.07514/) (2020)
- [Performance Guarantees for Spectral Initialization in Rotation Averaging and Pose-Graph SLAM](https://mlsanity.com/paper/2201.03773/) (2022)
- [Improved Performance Guarantees for Orthogonal Group Synchronization via Generalized Power Method](https://mlsanity.com/paper/2012.00470/) (2020)
- [Rotation Group Synchronization via Quotient Manifold](https://mlsanity.com/paper/2306.12730/) (2023)
- [Generalized Proximal Methods for Pose Graph Optimization](https://mlsanity.com/paper/2012.02709/) (2020)
- [A Power Method for Computing the Dominant Eigenvalue of a Dual Quaternion Hermitian Matrix](https://mlsanity.com/paper/2304.04355/) (2023)
- [Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM](https://mlsanity.com/paper/2404.18560/) (2024)

## 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)

Synchronization over the special Euclidean group SE(3) aims to recover absolute poses from noisy pairwise relative transformations and is a core primitive in robotics and 3D vision. Standard approaches often require multi-step heuristic procedures to recover valid poses, which are difficult to analyze and typically lack theoretical guarantees. This paper adopts a dual quaternion representation and formulates SE(3) synchronization directly over the unit dual quaternion. A two-stage algorithm is developed: A spectral initializer computed via the power method on a Hermitian dual quaternion measurement matrix, followed by a dual quaternion generalized power method (DQGPM) that enforces feasibility through per-iteration projection. The estimation error bounds are established for spectral estimators, and DQGPM is shown to admit a finite-iteration error bound and achieves linear error contraction up to an explicit noise-dependent threshold. Experiments on synthetic benchmarks and real-world multi-scan point-set registration demonstrate that the proposed pipeline improves both accuracy and efficiency over representative matrix-based methods.