Dual Quaternion SE(3) Synchronization with Recovery Guarantees

• URL: http://arxiv.org/abs/2602.00324v1
• Date: Fri, 30 Jan 2026 21:24:20 GMT
• Title: Dual Quaternion SE(3) Synchronization with Recovery Guarantees
• Abstract summary: This paper adopts a dual quaternion representation and formulates SE(3) synchronization directly over the unit dual quaternion.<n>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.<n>Experiments on synthetic benchmarks and real-world multi-scan point-set registration demonstrate that the proposed pipeline improves both accuracy and efficiency.
• Score: 18.75848171128639
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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