{"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/diffusion-shock-filtering-on-the-space-of","title":"Diffusion-Shock Filtering on the Space of Positions and Orientations","arxiv_id":"2502.17146","date":"2025-02-24","proceeding":null,"authors":["Finn M. Sherry","Kristina Schaefer","Remco Duits"],"abstract":"We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\\mathbb{R}^2$ to the space of positions and orientations $\\mathbb{M}_2 := \\mathbb{R}^2 \\times S^1$. This has numerous advantages, e.g. making it possible to enhance and inpaint crossing structures, since they become disentangled when lifted to $\\mathbb{M}_2$. We create a version of the algorithm using gauge frames to mitigate issues caused by lifting to a finite number of orientations. This leads us to study generalisations of diffusion, since the gauge frame diffusion is not generated by the Laplace-Beltrami operator. RDS filtering compares favourably to existing techniques such as Total Roto-Translational Variation (TR-TV) flow, NLM, and BM3D when denoising images with crossing structures, particularly if they are segmented. Additionally, we see that $\\mathbb{M}_2$ RDS inpainting is indeed able to restore crossing structures, unlike $\\mathbb{R}^2$ RDS inpainting.","url_abs":"https://arxiv.org/abs/2502.17146v2","url_pdf":"https://arxiv.org/pdf/2502.17146v2.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":"diffusion-shock-filtering-on-the-space-of","repo_url":"https://github.com/finnsherry/M2RDSFiltering","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}