Papers › ARCS: Accurate Rotation and Correspondence Search

ARCS: Accurate Rotation and Correspondence Search

28 Mar 2022CVPR 2022 1arXiv:2203.14493archive 2025-07-28

Liangzu Peng, Manolis C. Tsakiris, René Vidal

This paper is about the old Wahba problem in its more general form, which we call "simultaneous rotation and correspondence search". In this generalization we need to find a rotation that best aligns two partially overlapping $3$D point sets, of sizes m and n respectively with m≥n. We first propose a solver, ARCS, that i) assumes noiseless point sets in general position, ii) requires only $2$ inliers, iii) uses O(mlogm) time and O(m) space, and iv) can successfully solve the problem even with, e.g., m,n≈10⁶ in about $0.1$ seconds. We next robustify ARCS to noise, for which we approximately solve consensus maximization problems using ideas from robust subspace learning and interval stabbing. Thirdly, we refine the approximately found consensus set by a Riemannian subgradient descent approach over the space of unit quaternions, which we show converges globally to an ε-stationary point in O(ε⁻⁴) iterations, or locally to the ground-truth at a linear rate in the absence of noise. We combine these algorithms into ARCS+, to simultaneously search for rotations and correspondences. Experiments show that ARCS+ achieves state-of-the-art performance on large-scale datasets with more than 10⁶ points with a 10⁴ time-speedup over alternative methods. \url{https://github.com/liangzu/ARCS}

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