Dual Quaternion SE(3) Synchronization with Recovery Guarantees

TL;DR

This paper introduces a novel dual quaternion-based method for SE(3) synchronization that provides theoretical recovery guarantees and improves accuracy and efficiency in pose estimation tasks.

Contribution

It develops a two-stage algorithm with spectral initialization and a dual quaternion power method, offering explicit error bounds and convergence guarantees.

Findings

Improves accuracy over existing matrix-based methods.

Provides finite-iteration error bounds and linear convergence.

Demonstrates effectiveness on synthetic and real-world data.

Abstract

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.