{"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/memory-efficient-max-flow-for-multi-label","title":"Memory Efficient Max Flow for Multi-label Submodular MRFs","arxiv_id":"1702.05888","date":"2017-02-20","proceeding":"CVPR 2016 6","authors":["Thalaiyasingam Ajanthan","Richard Hartley","Mathieu Salzmann"],"abstract":"Multi-label submodular Markov Random Fields (MRFs) have been shown to be\nsolvable using max-flow based on an encoding of the labels proposed by\nIshikawa, in which each variable $X_i$ is represented by $\\ell$ nodes (where\n$\\ell$ is the number of labels) arranged in a column. However, this method in\ngeneral requires $2\\,\\ell^2$ edges for each pair of neighbouring variables.\nThis makes it inapplicable to realistic problems with many variables and\nlabels, due to excessive memory requirement. In this paper, we introduce a\nvariant of the max-flow algorithm that requires much less storage.\nConsequently, our algorithm makes it possible to optimally solve multi-label\nsubmodular problems involving large numbers of variables and labels on a\nstandard computer.","url_abs":"http://arxiv.org/abs/1702.05888v1","url_pdf":"http://arxiv.org/pdf/1702.05888v1.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":"memory-efficient-max-flow-for-multi-label","repo_url":"https://github.com/tajanthan/memf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}