{"id":"https://openalex.org/W2028384236","doi":"https://doi.org/10.1016/0031-3203(77)90007-3","title":"Metric invariants for unitary transformations and their application in character recognition","display_name":"Metric invariants for unitary transformations and their application in character recognition","publication_year":1977,"publication_date":"1977-01-01","ids":{"openalex":"https://openalex.org/W2028384236","doi":"https://doi.org/10.1016/0031-3203(77)90007-3","mag":"2028384236"},"language":"en","primary_location":{"id":"doi:10.1016/0031-3203(77)90007-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0031-3203(77)90007-3","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"},"type":"article","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/A5039458347","display_name":"Serge Wendling","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Wendling","raw_affiliation_strings":["Laboratoire d'Intelligence Artificielle, Universit\u00e9 de Besan\u00e7on, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Intelligence Artificielle, Universit\u00e9 de Besan\u00e7on, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090956498","display_name":"G\u00e9rard Gagneux","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Gagneux","raw_affiliation_strings":["Laboratoire d'Intelligence Artificielle, Universit\u00e9 de Besan\u00e7on, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Intelligence Artificielle, Universit\u00e9 de Besan\u00e7on, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2710,"currency":"USD","value_usd":2710},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1439034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"4","first_page":"233","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9273999929428101,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9273999929428101,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.9147999882698059,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9115999937057495,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/hadamard-transform","display_name":"Hadamard transform","score":0.7912397384643555},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7632954120635986},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7123781442642212},{"id":"https://openalex.org/keywords/unitary-transformation","display_name":"Unitary transformation","score":0.6843855381011963},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6146395802497864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5619943141937256},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.509515106678009},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.48331141471862793},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4774937331676483},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.45870694518089294},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4183829128742218},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40191519260406494},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23988661170005798},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10245019197463989},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08008107542991638},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06712377071380615}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7912397384643555},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7632954120635986},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7123781442642212},{"id":"https://openalex.org/C179371143","wikidata":"https://www.wikidata.org/wiki/Q2495534","display_name":"Unitary transformation","level":3,"score":0.6843855381011963},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6146395802497864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5619943141937256},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.509515106678009},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.48331141471862793},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4774937331676483},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.45870694518089294},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4183829128742218},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40191519260406494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23988661170005798},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10245019197463989},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08008107542991638},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06712377071380615},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0031-3203(77)90007-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0031-3203(77)90007-3","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W232468466","https://openalex.org/W1587863748","https://openalex.org/W2035991982","https://openalex.org/W2110460117","https://openalex.org/W6659383007","https://openalex.org/W6676741957"],"related_works":["https://openalex.org/W1986731917","https://openalex.org/W2087469844","https://openalex.org/W2119386911","https://openalex.org/W2375060996","https://openalex.org/W1973399563","https://openalex.org/W2626609153","https://openalex.org/W2074893110","https://openalex.org/W2107986711","https://openalex.org/W2039157269","https://openalex.org/W4221156334"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
