{"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/monge-kantorovich-quantiles-and-ranks-for","title":"Monge-Kantorovich quantiles and ranks for image data","arxiv_id":"2503.02427","date":"2025-03-04","proceeding":null,"authors":["Gauthier Thurin"],"abstract":"This paper defines quantiles, ranks and statistical depths for image data by leveraging ideas from measure transportation. The first step is to embed a distribution of images in a tangent space, with the framework of linear optimal transport. Therein, Monge-Kantorovich quantiles are shown to provide a meaningful ordering of image data, with outward images having unusual shapes. Numerical experiments showcase the relevance of the proposed procedure, for descriptive analysis, outlier detection or statistical testing.","url_abs":"https://arxiv.org/abs/2503.02427v1","url_pdf":"https://arxiv.org/pdf/2503.02427v1.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":"monge-kantorovich-quantiles-and-ranks-for","repo_url":"https://github.com/gauthierthurin/QuantilesForImages","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[],"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}