{"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/graduated-non-convexity-for-robust-spatial","title":"Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection","arxiv_id":"1909.08605","date":"2019-09-18","proceeding":null,"authors":["Heng Yang","Pasquale Antonante","Vasileios Tzoumas","Luca Carlone"],"abstract":"Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least-squares formulations, and, as a result, are brittle against outliers. While a standard approach to regain robustness against outliers is to use robust cost functions, the latter typically introduce other non-convexities, preventing the use of existing non-minimal solvers. In this paper, we enable the simultaneous use of non-minimal solvers and robust estimation by providing a general-purpose approach for robust global estimation, which can be applied to any problem where a non-minimal solver is available for the outlier-free case. To this end, we leverage the Black-Rangarajan duality between robust estimation and outlier processes (which has been traditionally applied to early vision problems), and show that graduated non-convexity (GNC) can be used in conjunction with non-minimal solvers to compute robust solutions, without requiring an initial guess. Although GNC's global optimality cannot be guaranteed, we demonstrate the empirical robustness of the resulting robust non-minimal solvers in applications, including point cloud and mesh registration, pose graph optimization, and image-based object pose estimation (also called shape alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC, are more accurate than specialized local solvers, and faster than specialized global solvers. We also propose the first certifiably optimal non-minimal solver for shape alignment using SOS relaxation.","url_abs":"https://arxiv.org/abs/1909.08605v4","url_pdf":"https://arxiv.org/pdf/1909.08605v4.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":"graduated-non-convexity-for-robust-spatial","repo_url":"https://github.com/MIT-SPARK/CertifiablyRobustPerception","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"graduated-non-convexity-for-robust-spatial","repo_url":"https://github.com/MIT-SPARK/GNC-and-ADAPT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"graduated-non-convexity-for-robust-spatial","repo_url":"https://github.com/MIT-SPARK/TEASER-plusplus","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"graduated-non-convexity-for-robust-spatial","repo_url":"https://github.com/StrikerCC/Teaser-plusplus-testing","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"pose-estimation","task_name":"Pose Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1909.08605","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}