{"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/domain-informed-spline-interpolation","title":"Domain-Informed Spline Interpolation","arxiv_id":"1810.07502","date":"2019-06-27","proceeding":null,"authors":[],"abstract":"Standard interpolation techniques are implicitly based on the assumption that\nthe signal lies on a single homogeneous domain. In contrast, many naturally\noccurring signals lie on an inhomogeneous domain, such as brain activity\nassociated to different brain tissue. We propose an interpolation method that\ninstead exploits prior information about domain inhomogeneity, characterized by\ndifferent, potentially overlapping, subdomains. As proof of concept, the focus\nis put on extending conventional shift-invariant B-spline interpolation. Given\na known inhomogeneous domain, B-spline interpolation of a given order is\nextended to a domain-informed, shift-variant interpolation. This is done by\nconstructing a domain-informed generating basis that satisfies stability\nproperties. We illustrate example constructions of domain-informed generating\nbasis, and show their property in increasing the coherence between the\ngenerating basis and the given inhomogeneous domain. By advantageously\nexploiting domain knowledge, we demonstrate the benefit of domain-informed\ninterpolation over standard B-spline interpolation through Monte Carlo\nsimulations across a range of B-spline orders. We also demonstrate the\nfeasibility of domain-informed interpolation in a neuroimaging application\nwhere the domain information is available by a complementary image contrast.\nThe results show the benefit of incorporating domain knowledge so that an\ninterpolant consistent to the anatomy of the brain is obtained.","url_abs":"http://arxiv.org/abs/1810.07502v3","url_pdf":"http://arxiv.org/pdf/1810.07502v3.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":"domain-informed-spline-interpolation","repo_url":"https://github.com/aitchbi/DIBSI","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"anatomy","task_name":"Anatomy"}],"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}