Dual Quaternion SE(3) Synchronization with Recovery Guarantees

2026-01-30

AI Summary

This work addresses the fundamental challenge of recovering absolute poses from noisy pairwise relative transformations in robotics and 3D vision. We propose a novel SE(3) synchronization method based on dual quaternions, which directly models the problem on the unit dual quaternion manifold. Our approach features a two-stage algorithm comprising spectral initialization followed by a Dual Quaternion Generalized Power Method (DQGPM), with iterative projection steps to enforce feasibility. Notably, this is the first method to provide finite-step error bounds and linear error contraction guarantees for SE(3) synchronization, circumventing the need for conventional multi-stage heuristic pipelines. Experiments on both synthetic data and real-world multi-frame point cloud registration demonstrate that our method significantly outperforms prevailing matrix-based approaches, achieving a unified improvement in accuracy, computational efficiency, and theoretical tractability.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: 3D Computer Vision
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• SE(3) synchronization
• absolute pose recovery
• noisy relative transformations
• dual quaternion
• pose estimation

Innovation

• dual quaternion
• SE(3) synchronization
• generalized power method
• spectral initialization
• error bound