{"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/deterministic-approximate-methods-for-maximum","title":"Deterministic Approximate Methods for Maximum Consensus Robust Fitting","arxiv_id":"1710.10003","date":"2017-10-27","proceeding":null,"authors":["Huu Le","Tat-Jun Chin","Anders Eriksson","Thanh-Toan Do","David Suter"],"abstract":"Maximum consensus estimation plays a critically important role in robust\nfitting problems in computer vision. Currently, the most prevalent algorithms\nfor consensus maximization draw from the class of randomized\nhypothesize-and-verify algorithms, which are cheap but can usually deliver only\nrough approximate solutions. On the other extreme, there are exact algorithms\nwhich are exhaustive search in nature and can be costly for practical-sized\ninputs. This paper fills the gap between the two extremes by proposing\ndeterministic algorithms to approximately optimize the maximum consensus\ncriterion. Our work begins by reformulating consensus maximization with linear\ncomplementarity constraints. Then, we develop two novel algorithms: one based\non non-smooth penalty method with a Frank-Wolfe style optimization scheme, the\nother based on the Alternating Direction Method of Multipliers (ADMM). Both\nalgorithms solve convex subproblems to efficiently perform the optimization. We\ndemonstrate the capability of our algorithms to greatly improve a rough initial\nestimate, such as those obtained using least squares or a randomized algorithm.\nCompared to the exact algorithms, our approach is much more practical on\nrealistic input sizes. Further, our approach is naturally applicable to\nestimation problems with geometric residuals","url_abs":"http://arxiv.org/abs/1710.10003v2","url_pdf":"http://arxiv.org/pdf/1710.10003v2.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":"deterministic-approximate-methods-for-maximum","repo_url":"https://github.com/ZhipengCai/Demo---Deterministic-consensus-maximization-with-biconvex-programming","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.10003","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}