{"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/max-normalized-radon-cumulative-distribution","title":"Max-Normalized Radon Cumulative Distribution Transform for Limited Data Classification","arxiv_id":"2411.16282","date":"2024-11-25","proceeding":null,"authors":["Matthias Beckmann","Robert Beinert","Jonas Bresch"],"abstract":"The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates classification tasks, especially in the small data regime, like the recognition of watermarks in filigranology. Here, a typical issue is that the given data may be subject to affine transformations caused by the measuring process. The aim of this paper is to make the R-CDT and the related sliced Wasserstein distance invariant under affine transformations. For this, we propose a two-step normalization of the R-CDT and prove that our novel transform allows linear separation of affinely transformed image classes. The theoretical results are supported by numerical experiments showing a significant increase of the classification accuracy compared to the original R-CDT.","url_abs":"https://arxiv.org/abs/2411.16282v1","url_pdf":"https://arxiv.org/pdf/2411.16282v1.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":"max-normalized-radon-cumulative-distribution","repo_url":"https://github.com/drbeckmann/nr-cdt","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":"https://app.syntology.ai/?focus=2411.16282","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}