{"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/variational-methods-for-normal-integration","title":"Variational Methods for Normal Integration","arxiv_id":"1709.05965","date":"2017-09-18","proceeding":null,"authors":["Yvain Quéau","Jean-Denis Durou","Jean-François Aujol"],"abstract":"The need for an efficient method of integration of a dense normal field is\ninspired by several computer vision tasks, such as shape-from-shading,\nphotometric stereo, deflectometry, etc. Inspired by edge-preserving methods\nfrom image processing, we study in this paper several variational approaches\nfor normal integration, with a focus on non-rectangular domains, free boundary\nand depth discontinuities. We first introduce a new discretization for\nquadratic integration, which is designed to ensure both fast recovery and the\nability to handle non-rectangular domains with a free boundary. Yet, with this\nsolver, discontinuous surfaces can be handled only if the scene is first\nsegmented into pieces without discontinuity. Hence, we then discuss several\ndiscontinuity-preserving strategies. Those inspired, respectively, by the\nMumford-Shah segmentation method and by anisotropic diffusion, are shown to be\nthe most effective for recovering discontinuities.","url_abs":"http://arxiv.org/abs/1709.05965v1","url_pdf":"http://arxiv.org/pdf/1709.05965v1.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":"variational-methods-for-normal-integration","repo_url":"https://github.com/yqueau/normal_integration","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"variational-methods-for-normal-integration","repo_url":"https://github.com/zhenzhangye/orthonormal_to_perspective","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.05965","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}