{"id":"https://openalex.org/W2054959112","doi":"https://doi.org/10.1142/s0219691310003493","title":"ON AN EFFICIENT SPARSE REPRESENTATION OF OBJECTS OF GENERAL SHAPE VIA CONTINUOUS EXTENSION AND WAVELET APPROXIMATION","display_name":"ON AN EFFICIENT SPARSE REPRESENTATION OF OBJECTS OF GENERAL SHAPE VIA CONTINUOUS EXTENSION AND WAVELET APPROXIMATION","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W2054959112","doi":"https://doi.org/10.1142/s0219691310003493","mag":"2054959112"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691310003493","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691310003493","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/A5067244173","display_name":"Naoki Saito","orcid":"https://orcid.org/0000-0001-5234-4719"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"NAOKI SAITO","raw_affiliation_strings":["Department of Mathematics, University of California, Davis, CA 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100393609","display_name":"Zhihua Zhang","orcid":"https://orcid.org/0000-0002-6449-4332"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ZHIHUA ZHANG","raw_affiliation_strings":["Department of Mathematics, University of California, Davis, CA 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Davis, CA 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":1.5868,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84515322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"08","issue":"02","first_page":"253","last_page":"269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9988999962806702,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9988999962806702,"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":0.9987999796867371,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9925000071525574,"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":0.8605315685272217},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.804085373878479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.601061999797821},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5801397562026978},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5784125924110413},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.5392654538154602},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5153602957725525},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4963250756263733},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.48375558853149414},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.46931028366088867},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3570535182952881},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33665746450424194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3127056360244751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29573917388916016},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2409990429878235},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0681164562702179}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.8605315685272217},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.804085373878479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.601061999797821},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5801397562026978},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5784125924110413},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5392654538154602},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5153602957725525},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4963250756263733},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.48375558853149414},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.46931028366088867},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3570535182952881},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33665746450424194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3127056360244751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29573917388916016},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2409990429878235},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0681164562702179},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691310003493","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691310003493","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1541134818","https://openalex.org/W1987634817","https://openalex.org/W2044562173","https://openalex.org/W2062015920","https://openalex.org/W2075223227","https://openalex.org/W2086465792","https://openalex.org/W2086921140","https://openalex.org/W2104095591","https://openalex.org/W2115755118","https://openalex.org/W3211330693","https://openalex.org/W4231428347"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2370289839","https://openalex.org/W2082716031","https://openalex.org/W2933494595","https://openalex.org/W4313347705","https://openalex.org/W3144842310","https://openalex.org/W2206006039","https://openalex.org/W3027905406"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,83,97,112],"discuss":[4],"the":[5,12,28,39,44,56,59,64,74,80,86,102,106],"continuous":[6],"extension":[7,45,65,75],"and":[8,49,100],"wavelet":[9,67,89,117],"approximation":[10],"of":[11,20,58,88,105],"detected":[13],"object":[14,107],"on":[15,38,69],"a":[16,31,47,115],"general":[17],"domain":[18],"\u03a9":[19],"\u211d":[21,70],"2":[22,71],".":[23,72],"We":[24,62],"first":[25],"extend":[26],"continuously":[27],"image":[29],"to":[30],"square":[32],"T":[33],"such":[34],"that":[35,85],"it":[36],"vanishes":[37],"boundary":[40,60],"\u2202T.":[41],"On":[42],"T\u2216\u03a9,":[43],"has":[46],"simple":[48],"clear":[50],"representation":[51],"which":[52],"is":[53,94],"determined":[54],"by":[55,79,92],"equation":[57],"\u2202\u03a9.":[61],"expand":[63],"into":[66],"series":[68],"Since":[73],"tools":[76],"are":[77],"polynomials,":[78],"moment":[81],"theorem,":[82],"know":[84],"sequence":[87],"coefficients":[90],"obtained":[91],"us":[93],"sparse.":[95],"Therefore,":[96],"can":[98],"approximate":[99],"analyze":[101],"internal":[103],"information":[104],"very":[108],"well":[109],"even":[110],"if":[111],"only":[113],"store":[114],"few":[116],"coefficients.":[118]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}