{"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/lifting-methods-for-manifold-valued","title":"Lifting methods for manifold-valued variational problems","arxiv_id":"1908.03776","date":"2019-08-10","proceeding":null,"authors":["Thomas Vogt","Evgeny Strekalovskiy","Daniel Cremers","Jan Lellmann"],"abstract":"Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum, which allows to find approximate global minimizers of the original problem. Recently, these techniques have also been applied to problems with values in a manifold. We provide a review of such methods in a refined framework based on a finite element discretization of the range, which extends the concept of sublabel-accurate lifting to manifolds. We also generalize existing methods for total variation regularization to support general convex regularization.","url_abs":"http://arxiv.org/abs/1908.03776v1","url_pdf":"http://arxiv.org/pdf/1908.03776v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"lifting-methods-for-manifold-valued","repo_url":"https://github.com/room-10/mfd-lifting","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}