{"id":"https://openalex.org/W4414250918","doi":"https://doi.org/10.1007/978-3-032-05060-1_32","title":"Beyond Splines: Legendre and\u00a0Shmaliy Polynomial-KANs for\u00a0Robust Image Recognition","display_name":"Beyond Splines: Legendre and\u00a0Shmaliy Polynomial-KANs for\u00a0Robust Image Recognition","publication_year":2025,"publication_date":"2025-09-16","ids":{"openalex":"https://openalex.org/W4414250918","doi":"https://doi.org/10.1007/978-3-032-05060-1_32"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-05060-1_32","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-05060-1_32","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004595910","display_name":"Jos\u00e9 Carlos Moreno-Tagle","orcid":null},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Carlos Moreno-Tagle","raw_affiliation_strings":["Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","Posgrado en Ciencia e Ingenier\u00eda de la Computaci\u00f3n, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":"https://orcid.org/0009-0001-0165-6373","affiliations":[{"raw_affiliation_string":"Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Posgrado en Ciencia e Ingenier\u00eda de la Computaci\u00f3n, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057830181","display_name":"Jimena Olveres","orcid":"https://orcid.org/0000-0002-1514-4520"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jimena Olveres","raw_affiliation_strings":["Centro de Estudios en Computaci\u00f3n Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-1514-4520","affiliations":[{"raw_affiliation_string":"Centro de Estudios en Computaci\u00f3n Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037203797","display_name":"Boris Escalante-Ram\u0131\u0301rez","orcid":"https://orcid.org/0000-0003-4936-8714"},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Boris Escalante-Ram\u00edrez","raw_affiliation_strings":["Centro de Estudios en Computaci\u00f3n Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico"],"raw_orcid":"https://orcid.org/0000-0003-4936-8714","affiliations":[{"raw_affiliation_string":"Centro de Estudios en Computaci\u00f3n Avanzada, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Departamento de Procesamiento de Se\u00f1ales, Facultad de Ingenier\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, Mexico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004595910"],"corresponding_institution_ids":["https://openalex.org/I8961855"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35164536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"373","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12702","display_name":"Brain Tumor Detection and Classification","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12702","display_name":"Brain Tumor Detection and Classification","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.9635999798774719},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.8173999786376953},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.7443000078201294},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5532000064849854},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5008999705314636},{"id":"https://openalex.org/keywords/zernike-polynomials","display_name":"Zernike polynomials","score":0.49950000643730164},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.44190001487731934},{"id":"https://openalex.org/keywords/legendre-function","display_name":"Legendre function","score":0.4327999949455261}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.9635999798774719},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.8173999786376953},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.7443000078201294},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5532000064849854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5382000207901001},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.49950000643730164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4593000113964081},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.4327999949455261},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42320001125335693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4171999990940094},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.4090999960899353},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.33399999141693115},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33399999141693115},{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.32170000672340393},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.29750001430511475},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.27459999918937683},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.2705000042915344}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-05060-1_32","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-05060-1_32","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W358380361","https://openalex.org/W1509691074","https://openalex.org/W2018015124","https://openalex.org/W2051182150","https://openalex.org/W2057897480","https://openalex.org/W3095948197","https://openalex.org/W3164330620","https://openalex.org/W4317436377","https://openalex.org/W4408631936"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}