{"id":"https://openalex.org/W1978682680","doi":"https://doi.org/10.3390/a2041263","title":"Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures","display_name":"Compound Biorthogonal Wavelets on Quadrilaterals and Polar Structures","publication_year":2009,"publication_date":"2009-09-28","ids":{"openalex":"https://openalex.org/W1978682680","doi":"https://doi.org/10.3390/a2041263","mag":"1978682680"},"language":"en","primary_location":{"id":"doi:10.3390/a2041263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2041263","pdf_url":"https://www.mdpi.com/1999-4893/2/4/1263/pdf?version=1254136695","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/2/4/1263/pdf?version=1254136695","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076987947","display_name":"Chong Zhao","orcid":"https://orcid.org/0000-0002-9655-6454"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chong Zhao","raw_affiliation_strings":["Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359489","display_name":"Hanqiu Sun","orcid":"https://orcid.org/0000-0002-3244-4111"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hanqiu Sun","raw_affiliation_strings":["Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Engineering, The Chinese University of Hong Kong, The Chinese University of Hong Kong, Shatin N.T., Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100701119","display_name":"Huawei Wang","orcid":"https://orcid.org/0000-0002-9279-4789"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Huawei Wang","raw_affiliation_strings":["Department of MEEM, The City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of MEEM, The City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023893248","display_name":"Kaihuai Qin","orcid":"https://orcid.org/0000-0001-8902-142X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaihuai Qin","raw_affiliation_strings":["Department of Computer Science and Technology, East Main Building, Tsinghua University, Beijing 100084, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, East Main Building, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5076987947"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09275731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"4","first_page":"1263","last_page":"1280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9947999715805054,"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/T13579","display_name":"Image and Video Stabilization","score":0.991599977016449,"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/wavelet","display_name":"Wavelet","score":0.7970744371414185},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.7966198921203613},{"id":"https://openalex.org/keywords/biorthogonal-wavelet","display_name":"Biorthogonal wavelet","score":0.6187694072723389},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.5871240496635437},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.5839509963989258},{"id":"https://openalex.org/keywords/biorthogonal-system","display_name":"Biorthogonal system","score":0.5268016457557678},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.49452921748161316},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.47045576572418213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4345018267631531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38291722536087036},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.341621994972229},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3259352743625641},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.26822707056999207},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1955096423625946},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.19293493032455444},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17210331559181213},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.13727235794067383},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1347116231918335}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7970744371414185},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.7966198921203613},{"id":"https://openalex.org/C2778869661","wikidata":"https://www.wikidata.org/wiki/Q4915256","display_name":"Biorthogonal wavelet","level":5,"score":0.6187694072723389},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.5871240496635437},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.5839509963989258},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.5268016457557678},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.49452921748161316},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.47045576572418213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4345018267631531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38291722536087036},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.341621994972229},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3259352743625641},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.26822707056999207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1955096423625946},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.19293493032455444},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17210331559181213},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.13727235794067383},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1347116231918335},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a2041263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2041263","pdf_url":"https://www.mdpi.com/1999-4893/2/4/1263/pdf?version=1254136695","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c1968fd30e4544eebd9254ad3caad914","is_oa":true,"landing_page_url":"https://doaj.org/article/c1968fd30e4544eebd9254ad3caad914","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 2, Iss 4, Pp 1263-1280 (2009)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/2/4/1263/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a2041263","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"},{"id":"pmh:oai:pure.atira.dk:publications/1cb7bf5c-83e2-447b-ab29-44be8bcc91bd","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/1cb7bf5c-83e2-447b-ab29-44be8bcc91bd","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Zhao, C, Sun, H, Wang, H & Qin, K 2009, 'Compound biorthogonalwavelets on quadrilaterals and polar structures', Algorithms, vol. 2, no. 4, pp. 1263-1280. https://doi.org/10.3390/a2041263","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a2041263","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2041263","pdf_url":"https://www.mdpi.com/1999-4893/2/4/1263/pdf?version=1254136695","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1978682680.pdf","grobid_xml":"https://content.openalex.org/works/W1978682680.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1584452409","https://openalex.org/W1976957312","https://openalex.org/W1985812168","https://openalex.org/W1989480677","https://openalex.org/W1998941214","https://openalex.org/W2012909180","https://openalex.org/W2014134723","https://openalex.org/W2090387084","https://openalex.org/W2117028583","https://openalex.org/W2117188745","https://openalex.org/W2125481678","https://openalex.org/W2151568950","https://openalex.org/W2154320156","https://openalex.org/W2162677913","https://openalex.org/W2163324644","https://openalex.org/W2166145165","https://openalex.org/W2783009114","https://openalex.org/W3149831928","https://openalex.org/W3160210108","https://openalex.org/W6634864180","https://openalex.org/W6647637797"],"related_works":["https://openalex.org/W2106250363","https://openalex.org/W2127433149","https://openalex.org/W2804200484","https://openalex.org/W2123651802","https://openalex.org/W199025143","https://openalex.org/W2090113569","https://openalex.org/W2136651366","https://openalex.org/W2373121303","https://openalex.org/W2377463317","https://openalex.org/W2163980049"],"abstract_inverted_index":{"In":[0,24],"geometric":[1],"models":[2,90,123],"with":[3,12,45,91,98],"high-valence":[4,59],"vertices,":[5],"current":[6],"subdivision":[7,33,50,55,70,100,118],"wavelets":[8,105,119],"may":[9,71],"not":[10],"deal":[11],"the":[13,29,42,58,63,84,104,117,148],"special":[14,81],"cases":[15],"well":[16],"for":[17,121],"good":[18],"visual":[19],"effect":[20],"of":[21,111,132,150],"multiresolution":[22],"surfaces.":[23],"this":[25],"paper,":[26],"we":[27,102],"present":[28],"novel":[30],"biorthogonal":[31],"polar":[32,46,49,75,85,112,128],"wavelets,":[34],"which":[35],"can":[36,51,115],"efficiently":[37],"perform":[38],"wavelet":[39,78,133],"analysis":[40,134],"to":[41,89],"control":[43],"nets":[44],"structures.":[47,129],"The":[48,130,143],"generate":[52],"more":[53],"natural":[54],"surfaces":[56],"around":[57],"vertices":[60],"and":[61,65,108,127,135,140],"avoid":[62],"ripples":[64],"saddle":[66],"points":[67],"where":[68],"Catmull-Clark":[69,99],"produce.":[72],"Based":[73],"on":[74,83],"subdivision,":[76],"our":[77,151],"scheme":[79],"supports":[80],"operations":[82],"structures,":[86,113],"especially":[87],"suitable":[88],"many":[92],"facets":[93],"joining.":[94],"For":[95],"seamless":[96],"fusing":[97],"wavelet,":[101],"construct":[103],"in":[106],"circular":[107],"radial":[109],"layers":[110],"so":[114],"combine":[116],"smoothly":[120],"composite":[122],"formed":[124],"by":[125],"quadrilaterals":[126],"computations":[131],"synthesis":[136],"are":[137],"highly":[138],"efficient":[139],"fully":[141],"in-place.":[142],"experimental":[144],"results":[145],"have":[146],"confirmed":[147],"stability":[149],"proposed":[152],"approach.":[153]},"counts_by_year":[],"updated_date":"2026-03-05T09:29:38.588285","created_date":"2025-10-10T00:00:00"}
