{"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/multiscale-strategies-for-computing-optimal","title":"Multiscale Strategies for Computing Optimal Transport","arxiv_id":"1708.02469","date":"2017-08-08","proceeding":null,"authors":["Samuel Gerber","Mauro Maggioni"],"abstract":"This paper presents a multiscale approach to efficiently compute approximate\noptimal transport plans between point sets. It is particularly well-suited for\npoint sets that are in high-dimensions, but are close to being intrinsically\nlow-dimensional. The approach is based on an adaptive multiscale decomposition\nof the point sets. The multiscale decomposition yields a sequence of optimal\ntransport problems, that are solved in a top-to-bottom fashion from the\ncoarsest to the finest scale. We provide numerical evidence that this\nmultiscale approach scales approximately linearly, in time and memory, in the\nnumber of nodes, instead of quadratically or worse for a direct solution.\nEmpirically, the multiscale approach results in less than one percent relative\nerror in the objective function. Furthermore, the multiscale plans constructed\nare of interest by themselves as they may be used to introduce novel features\nand notions of distances between point sets. An analysis of sets of brain MRI\nbased on optimal transport distances illustrates the effectiveness of the\nproposed method on a real world data set. The application demonstrates that\nmultiscale optimal transport distances have the potential to improve on\nstate-of-the-art metrics currently used in computational anatomy.","url_abs":"http://arxiv.org/abs/1708.02469v1","url_pdf":"http://arxiv.org/pdf/1708.02469v1.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":"multiscale-strategies-for-computing-optimal","repo_url":"https://bitbucket.org/suppechasper/optimaltransport","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"multiscale-strategies-for-computing-optimal","repo_url":"https://github.com/samuelgerber/mop","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"anatomy","task_name":"Anatomy"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1708.02469","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}