{"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/the-matching-problem-between-functional","title":"The matching problem between functional shapes via a BV penalty term: a $Γ$-convergence result","arxiv_id":"1503.07685","date":"2015-03-26","proceeding":null,"authors":["G. Nardi","B. Charlier","A. Trouvé"],"abstract":"This paper proves a $\\Gamma$-convergence result for the discrete energy (to the continuous one) of the matching problem for signals defined on surfaces. In particular, we highlight some geometric properties that must be guaranteed in the discretization process to ensure the convergence of minimizers. The proof is given in the framework of functional shapes introduced in \\cite{ABN}. In particular, we consider a varifold-type attachment term, and a $BV$ penalty term is used instead of the original $L^2$ norm.","url_abs":"https://arxiv.org/abs/1503.07685v6","url_pdf":"https://arxiv.org/pdf/1503.07685v6.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":"the-matching-problem-between-functional","repo_url":"https://github.com/fshapes/fshapesTk","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}