{"id":"https://openalex.org/W2022284055","doi":"https://doi.org/10.1145/1937728.1937755","title":"Fourband multiwavelet series and orthogonal analysis for geometric shape","display_name":"Fourband multiwavelet series and orthogonal analysis for geometric shape","publication_year":2010,"publication_date":"2010-12-30","ids":{"openalex":"https://openalex.org/W2022284055","doi":"https://doi.org/10.1145/1937728.1937755","mag":"2022284055"},"language":"en","primary_location":{"id":"doi:10.1145/1937728.1937755","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1937728.1937755","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Second International Conference on Internet Multimedia Computing and Service","raw_type":"proceedings-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":null,"display_name":"Xiong Gang-Qiang","orcid":null},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiong Gang-Qiang","raw_affiliation_strings":["Sun Yat-Sen University, Guangzhou, China","[Sun Yat-sen University, Guangzhou, China.]"],"affiliations":[{"raw_affiliation_string":"Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"[Sun Yat-sen University, Guangzhou, China.]","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026248300","display_name":"Dongxu Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I111950717","display_name":"Macau University of Science and Technology","ror":"https://ror.org/03jqs2n27","country_code":"MO","type":"education","lineage":["https://openalex.org/I111950717","https://openalex.org/I4391767947"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Qi Dong-Xu","raw_affiliation_strings":["Sun Yat-Sen University, Guangzhou, China and Macao University of Science and Technology, Macao, China"],"affiliations":[{"raw_affiliation_string":"Sun Yat-Sen University, Guangzhou, China and Macao University of Science and Technology, Macao, China","institution_ids":["https://openalex.org/I111950717"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10832924,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"112","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9962000250816345,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9951000213623047,"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/gibbs-phenomenon","display_name":"Gibbs phenomenon","score":0.8889469504356384},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6628631353378296},{"id":"https://openalex.org/keywords/walsh-function","display_name":"Walsh function","score":0.643310010433197},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5826069712638855},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.573081910610199},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5475396513938904},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.5415071249008179},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5027179718017578},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4904918074607849},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.43990641832351685},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.42088061571121216},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4193258583545685},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.418911874294281},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4116653501987457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38191133737564087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3291659355163574},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1849237084388733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1813657283782959},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18063423037528992}],"concepts":[{"id":"https://openalex.org/C149568634","wikidata":"https://www.wikidata.org/wiki/Q5374","display_name":"Gibbs phenomenon","level":3,"score":0.8889469504356384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6628631353378296},{"id":"https://openalex.org/C164319782","wikidata":"https://www.wikidata.org/wiki/Q1934233","display_name":"Walsh function","level":2,"score":0.643310010433197},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5826069712638855},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.573081910610199},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5475396513938904},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5415071249008179},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5027179718017578},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4904918074607849},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.43990641832351685},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.42088061571121216},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4193258583545685},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.418911874294281},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4116653501987457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38191133737564087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3291659355163574},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1849237084388733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1813657283782959},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18063423037528992},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1937728.1937755","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1937728.1937755","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Second International Conference on Internet Multimedia Computing and Service","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W111918310","https://openalex.org/W1498717371","https://openalex.org/W1558047356","https://openalex.org/W1970297865","https://openalex.org/W1985059755","https://openalex.org/W1990157715","https://openalex.org/W2033838007","https://openalex.org/W2048247182","https://openalex.org/W2068422790","https://openalex.org/W2092897723","https://openalex.org/W2100917607","https://openalex.org/W2109411320","https://openalex.org/W2116124511","https://openalex.org/W2163964097","https://openalex.org/W2379585341","https://openalex.org/W2387697353","https://openalex.org/W2557333712","https://openalex.org/W7053384626"],"related_works":["https://openalex.org/W2388109326","https://openalex.org/W1963709166","https://openalex.org/W3017026799","https://openalex.org/W6842695","https://openalex.org/W3115000842","https://openalex.org/W4383032112","https://openalex.org/W2006465730","https://openalex.org/W2043867390","https://openalex.org/W4281263164","https://openalex.org/W105062963"],"abstract_inverted_index":{"This":[0],"paper":[1],"constructs":[2],"a":[3,84,94,144],"class":[4,85,95,145],"of":[5,26,64,86,96,112,118,146],"fourband":[6],"piecewise":[7],"polynomials":[8],"multiwavelets":[9],"(abbreviated":[10],"as":[11],"QVLets),":[12],"whose":[13],"scaling":[14],"functions":[15,18],"and":[16,22,28,36,48,51,82,102,121,140],"wavelet":[17],"have":[19],"explicit":[20],"expressions,":[21],"its":[23,52],"wavelets":[24],"consist":[25],"continuous":[27],"discontinuous":[29],"functions.":[30],"Unlike":[31],"Fourier":[32],"trigonometric,":[33],"Walsh":[34,120],"system":[35],"V":[37,122],"system,":[38],"there":[39],"is":[40,55,114],"no":[41],"Gibbs":[42],"phenomenon":[43],"at":[44],"breakpoints":[45],"or":[46,71],"endpoints":[47],"\"singular\"":[49],"phenomenon,":[50],"approximation":[53,110],"error":[54,111],"very":[56],"small":[57],"also,":[58],"if":[59],"we":[60,74,105],"apply":[61],"partial":[62],"sum":[63],"QVLets":[65,76,113],"series":[66],"to":[67,78],"represent":[68],"planar":[69],"curves":[70],"surfaces.":[72],"Afterwards,":[73],"use":[75],"coefficients":[77],"analyze":[79],"image":[80],"shape,":[81],"obtain":[83],"shape":[87],"descriptors,":[88,91],"i.e.,":[89],"QV":[90,138,141],"which":[92],"are":[93,143],"invariants":[97],"based":[98],"on":[99],"translation,":[100],"scale":[101],"rotation.":[103],"Finally,":[104],"confirm":[106],"with":[107],"experiments":[108],"that":[109,117,129],"less":[115],"than":[116],"Fourier,":[119],"system;":[123],"the":[124,130],"experimental":[125],"result":[126],"also":[127],"indicates":[128],"difference":[131],"between":[132],"images":[133],"can":[134],"be":[135],"illustrated":[136],"by":[137],"distance,":[139],"descriptors":[142],"feature":[147],"invariants.":[148]},"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}