{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/arcs-accurate-rotation-and-correspondence","title":"ARCS: Accurate Rotation and Correspondence Search","arxiv_id":"2203.14493","date":"2022-03-28","proceeding":"CVPR 2022 1","authors":["Liangzu Peng","Manolis C. Tsakiris","René Vidal"],"abstract":"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 $m\\geq n$. We first propose a solver, $\\texttt{ARCS}$, that i) assumes noiseless point sets in general position, ii) requires only $2$ inliers, iii) uses $O(m\\log m)$ time and $O(m)$ space, and iv) can successfully solve the problem even with, e.g., $m,n\\approx 10^6$ in about $0.1$ seconds. We next robustify $\\texttt{ARCS}$ 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 $\\varepsilon$-stationary point in $O(\\varepsilon^{-4})$ iterations, or locally to the ground-truth at a linear rate in the absence of noise. We combine these algorithms into $\\texttt{ARCS+}$, to simultaneously search for rotations and correspondences. Experiments show that $\\texttt{ARCS+}$ achieves state-of-the-art performance on large-scale datasets with more than $10^6$ points with a $10^4$ time-speedup over alternative methods. \\url{https://github.com/liangzu/ARCS}","url_abs":"https://arxiv.org/abs/2203.14493v2","url_pdf":"https://arxiv.org/pdf/2203.14493v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"arcs-accurate-rotation-and-correspondence","repo_url":"https://github.com/liangzu/arcs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2203.14493","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2203.14493"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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