Dual Quaternion SE(3) Synchronization with Recovery Guarantees
This work addresses a fundamental challenge in robotics and 3D vision by providing a theoretically guaranteed method for pose recovery, though it is incremental as it builds on existing synchronization techniques with a new representation.
The paper tackles the problem of recovering absolute poses from noisy pairwise relative transformations in SE(3) synchronization, a core task in robotics and 3D vision, by developing a dual quaternion-based algorithm that improves accuracy and efficiency over existing methods, as demonstrated in experiments.
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.