{"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/sublabel-accurate-relaxation-of-nonconvex","title":"Sublabel-Accurate Relaxation of Nonconvex Energies","arxiv_id":"1512.01383","date":"2015-12-04","proceeding":"CVPR 2016 6","authors":["Thomas Möllenhoff","Emanuel Laude","Michael Moeller","Jan Lellmann","Daniel Cremers"],"abstract":"We propose a novel spatially continuous framework for convex relaxations\nbased on functional lifting. Our method can be interpreted as a\nsublabel-accurate solution to multilabel problems. We show that previously\nproposed functional lifting methods optimize an energy which is linear between\ntwo labels and hence require (often infinitely) many labels for a faithful\napproximation. In contrast, the proposed formulation is based on a piecewise\nconvex approximation and therefore needs far fewer labels. In comparison to\nrecent MRF-based approaches, our method is formulated in a spatially continuous\nsetting and shows less grid bias. Moreover, in a local sense, our formulation\nis the tightest possible convex relaxation. It is easy to implement and allows\nan efficient primal-dual optimization on GPUs. We show the effectiveness of our\napproach on several computer vision problems.","url_abs":"http://arxiv.org/abs/1512.01383v1","url_pdf":"http://arxiv.org/pdf/1512.01383v1.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":"sublabel-accurate-relaxation-of-nonconvex","repo_url":"https://github.com/tum-vision/sublabel_relax","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"sublabel-accurate-relaxation-of-nonconvex","repo_url":"https://github.com/nurlanov-zh/sublabel-accurate-alpha-expansion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1512.01383","atlas_url":"https://app.syntology.ai/?focus=1512.01383","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}