{"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-convex-relaxation-of","title":"Sublabel-Accurate Convex Relaxation of Vectorial Multilabel Energies","arxiv_id":"1604.01980","date":"2016-04-07","proceeding":null,"authors":["Emanuel Laude","Thomas Möllenhoff","Michael Moeller","Jan Lellmann","Daniel Cremers"],"abstract":"Convex relaxations of nonconvex multilabel problems have been demonstrated to\nproduce superior (provably optimal or near-optimal) solutions to a variety of\nclassical computer vision problems. Yet, they are of limited practical use as\nthey require a fine discretization of the label space, entailing a huge demand\nin memory and runtime. In this work, we propose the first sublabel accurate\nconvex relaxation for vectorial multilabel problems. The key idea is that we\napproximate the dataterm of the vectorial labeling problem in a piecewise\nconvex (rather than piecewise linear) manner. As a result we have a more\nfaithful approximation of the original cost function that provides a meaningful\ninterpretation for the fractional solutions of the relaxed convex problem. In\nnumerous experiments on large-displacement optical flow estimation and on color\nimage denoising we demonstrate that the computed solutions have superior\nquality while requiring much lower memory and runtime.","url_abs":"http://arxiv.org/abs/1604.01980v2","url_pdf":"http://arxiv.org/pdf/1604.01980v2.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-convex-relaxation-of","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"}}],"tasks":[{"task_slug":"color-image-denoising","task_name":"Color Image Denoising"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"optical-flow-estimation","task_name":"Optical Flow Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}