{"id":"https://openalex.org/W1975989479","doi":"https://doi.org/10.1142/s021969131250052x","title":"LOCAL WAVELET TRANSFORM ON THE SMOOTH SURFACE OF ROTATION CLASS","display_name":"LOCAL WAVELET TRANSFORM ON THE SMOOTH SURFACE OF ROTATION CLASS","publication_year":2012,"publication_date":"2012-09-25","ids":{"openalex":"https://openalex.org/W1975989479","doi":"https://doi.org/10.1142/s021969131250052x","mag":"1975989479"},"language":"en","primary_location":{"id":"doi:10.1142/s021969131250052x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969131250052x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5088206330","display_name":"Baoqin Wang","orcid":"https://orcid.org/0000-0002-2197-0722"},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BAOQIN WANG","raw_affiliation_strings":["School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China","institution_ids":["https://openalex.org/I1334729051"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101430286","display_name":"Wang Gang","orcid":"https://orcid.org/0000-0003-3970-3734"},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"GANG WANG","raw_affiliation_strings":["School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China","institution_ids":["https://openalex.org/I1334729051"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024690699","display_name":"Xiaohui Zhou","orcid":"https://orcid.org/0000-0002-7189-0915"},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIAOHUI ZHOU","raw_affiliation_strings":["School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China","institution_ids":["https://openalex.org/I1334729051"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1334729051"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06507945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"06","first_page":"1250052","last_page":"1250052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9818000197410583,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9736999869346619,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flattening","display_name":"Flattening","score":0.7430423498153687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7365399599075317},{"id":"https://openalex.org/keywords/eulers-rotation-theorem","display_name":"Euler's rotation theorem","score":0.7165457010269165},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.6536879539489746},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5728793740272522},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5331432223320007},{"id":"https://openalex.org/keywords/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.4696435332298279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46149858832359314},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4606497287750244},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.4362507462501526},{"id":"https://openalex.org/keywords/integral-transform","display_name":"Integral transform","score":0.41396385431289673},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37767112255096436},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14654338359832764},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12449756264686584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09809675812721252}],"concepts":[{"id":"https://openalex.org/C19444555","wikidata":"https://www.wikidata.org/wiki/Q212750","display_name":"Flattening","level":2,"score":0.7430423498153687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7365399599075317},{"id":"https://openalex.org/C88977231","wikidata":"https://www.wikidata.org/wiki/Q681406","display_name":"Euler's rotation theorem","level":3,"score":0.7165457010269165},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.6536879539489746},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5728793740272522},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5331432223320007},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.4696435332298279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46149858832359314},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4606497287750244},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.4362507462501526},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.41396385431289673},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37767112255096436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14654338359832764},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12449756264686584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09809675812721252},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021969131250052x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969131250052x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1972640073","https://openalex.org/W1976170879","https://openalex.org/W1984032850","https://openalex.org/W2034651366","https://openalex.org/W2063616966","https://openalex.org/W2092939350","https://openalex.org/W2096897625","https://openalex.org/W2097221133","https://openalex.org/W2136463719","https://openalex.org/W2155791285","https://openalex.org/W4210770595"],"related_works":["https://openalex.org/W2101997086","https://openalex.org/W2088723847","https://openalex.org/W2382490471","https://openalex.org/W2085792030","https://openalex.org/W2120966954","https://openalex.org/W2368320199","https://openalex.org/W4233635293","https://openalex.org/W1986475093","https://openalex.org/W2406541087","https://openalex.org/W2759775138"],"abstract_inverted_index":{"For":[0,65],"the":[1,8,22,29,34,50,66,70,82,89,92,109,115,126,131,137],"smooth":[2,41],"surface":[3,42,74,119],"of":[4,11,21,44,69,91,102,130],"rotation":[5,45,73,78,118,123],"class":[6,46],"M,":[7],"explicit":[9],"construction":[10,90],"two":[12,67,83],"local":[13,35,51,84,93,99,110,132],"flattening":[14,36,85],"maps":[15,86],"p":[16,25,32,87],"are":[17],"given.":[18],"By":[19],"virtue":[20],"inverse":[23,127],"projection":[24,31],"-1":[26],",":[27],"where":[28],"bijection":[30],"is":[33,95,104,140],"map":[37],"from":[38,59],"a":[39,48,63],"two-dimensional":[40],"M":[43,55],"to":[47],"plane,":[49],"wavelet":[52,60,100,111,133],"transform":[53,61,101,128],"on":[54,62,114],"can":[56],"be":[57],"generated":[58],"plane.":[64],"examples":[68],"quadratic":[71,116],"parameter":[72,117],"and":[75,98,120],"parabolic":[76,121],"general":[77,122],"surface,":[79],"by":[80],"using":[81],"respectively,":[88],"dilation":[94],"systematically":[96],"studied,":[97],"them":[103],"offered.":[105,142],"We":[106],"also":[107,141],"show":[108],"graphical":[112],"representation":[113],"surface.":[124],"Finally,":[125],"formula":[129,139],"transform,":[134],"that":[135],"is,":[136],"reconstruction":[138]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}