{"id":"https://openalex.org/W1996338180","doi":"https://doi.org/10.1142/s0218001400000581","title":"ON GEOMETRIC AND ORTHOGONAL MOMENTS","display_name":"ON GEOMETRIC AND ORTHOGONAL MOMENTS","publication_year":2000,"publication_date":"2000-11-01","ids":{"openalex":"https://openalex.org/W1996338180","doi":"https://doi.org/10.1142/s0218001400000581","mag":"1996338180"},"language":"en","primary_location":{"id":"doi:10.1142/s0218001400000581","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218001400000581","pdf_url":null,"source":{"id":"https://openalex.org/S41486457","display_name":"International Journal of Pattern Recognition and Artificial Intelligence","issn_l":"0218-0014","issn":["0218-0014","1793-6381"],"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 Pattern Recognition and Artificial Intelligence","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/A5031318875","display_name":"Jun Shen","orcid":"https://orcid.org/0000-0002-9403-7140"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"JUN SHEN","raw_affiliation_strings":["Image Laboratory, Institute EGID, Bordeaux-3 University, All\u00e9e F. Daguin, 33607 Pessac, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Image Laboratory, Institute EGID, Bordeaux-3 University, All\u00e9e F. Daguin, 33607 Pessac, France","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013863365","display_name":"Weifeng Shen","orcid":"https://orcid.org/0000-0002-0418-6848"},"institutions":[{"id":"https://openalex.org/I4210127074","display_name":"Zhongshan Hospital","ror":"https://ror.org/032x22645","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210127074"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"WEI SHEN","raw_affiliation_strings":["Department of Electronics, Zhongshan University, Canton, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Zhongshan University, Canton, P.R. China","institution_ids":["https://openalex.org/I4210127074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070729773","display_name":"Danfei Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"DANFEI SHEN","raw_affiliation_strings":["Ecole Nationale Sup\u00e9rieure des T\u00e9l\u00e9communications, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Nationale Sup\u00e9rieure des T\u00e9l\u00e9communications, Paris, France","institution_ids":["https://openalex.org/I12356871"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3853,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.68152429,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"07","first_page":"875","last_page":"894"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9994999766349792,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9994999766349792,"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/T13114","display_name":"Image Processing Techniques and Applications","score":0.9878000020980835,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9837999939918518,"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/hermite-polynomials","display_name":"Hermite polynomials","score":0.8296140432357788},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.7824124097824097},{"id":"https://openalex.org/keywords/velocity-moments","display_name":"Velocity Moments","score":0.7186242938041687},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6977227926254272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6274410486221313},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5724042057991028},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.5508055686950684},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5321077108383179},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5193784832954407},{"id":"https://openalex.org/keywords/image-moment","display_name":"Image moment","score":0.4366525411605835},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41766366362571716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35269543528556824},{"id":"https://openalex.org/keywords/zernike-polynomials","display_name":"Zernike polynomials","score":0.33634063601493835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31013423204421997},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.28293415904045105},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.2757170796394348},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25837719440460205},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.23062098026275635},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22822067141532898},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.13070377707481384},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09103912115097046},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07695263624191284}],"concepts":[{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8296140432357788},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7824124097824097},{"id":"https://openalex.org/C149539972","wikidata":"https://www.wikidata.org/wiki/Q7919290","display_name":"Velocity Moments","level":4,"score":0.7186242938041687},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6977227926254272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6274410486221313},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5724042057991028},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5508055686950684},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5321077108383179},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5193784832954407},{"id":"https://openalex.org/C108311513","wikidata":"https://www.wikidata.org/wiki/Q841934","display_name":"Image moment","level":4,"score":0.4366525411605835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41766366362571716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35269543528556824},{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.33634063601493835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31013423204421997},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.28293415904045105},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.2757170796394348},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25837719440460205},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.23062098026275635},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22822067141532898},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.13070377707481384},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09103912115097046},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07695263624191284},{"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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C165699331","wikidata":"https://www.wikidata.org/wiki/Q461533","display_name":"Wavefront","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218001400000581","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218001400000581","pdf_url":null,"source":{"id":"https://openalex.org/S41486457","display_name":"International Journal of Pattern Recognition and Artificial Intelligence","issn_l":"0218-0014","issn":["0218-0014","1793-6381"],"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 Pattern Recognition and Artificial Intelligence","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":7,"referenced_works":["https://openalex.org/W1970097244","https://openalex.org/W2034780515","https://openalex.org/W2096889917","https://openalex.org/W2104775941","https://openalex.org/W2139828242","https://openalex.org/W2146880335","https://openalex.org/W2166617644"],"related_works":["https://openalex.org/W2040708001","https://openalex.org/W2010004168","https://openalex.org/W2122970665","https://openalex.org/W2736737644","https://openalex.org/W92676756","https://openalex.org/W2129460581","https://openalex.org/W2086936614","https://openalex.org/W1965081020","https://openalex.org/W2145067269","https://openalex.org/W1671010100"],"abstract_inverted_index":{"Moments":[0],"are":[1,108,113,194],"widely":[2],"used":[3],"in":[4,28,60,136],"pattern":[5,98],"recognition,":[6],"image":[7,87],"processing,":[8],"computer":[9],"vision":[10],"and":[11,16,37,48,51,78,100,119,140,147],"multiresolution":[12],"analysis.":[13,178],"To":[14],"clarify":[15],"to":[17,44,117,169],"guide":[18],"the":[19,34,121,131,174],"use":[20],"of":[21,24,70,76,134,150,176],"different":[22,35,71,74,80,91,151,154],"types":[23],"moments,":[25],"we":[26,54],"present":[27,166],"this":[29],"paper":[30],"a":[31],"study":[32],"on":[33,90],"moments":[36,50,135,149,165],"compare":[38],"their":[39,52,58],"behavior.":[40],"After":[41],"an":[42,167],"introduction":[43],"geometric,":[45],"Legendre,":[46],"Hermite":[47],"Gaussian\u2013Hermite":[49,104,148,164],"calculation,":[53],"analyze":[55,130],"at":[56],"first":[57],"behavior":[59,133],"spatial":[61],"domain.":[62,138],"Our":[63,186],"analysis":[64,99,187],"shows":[65],"orthogonal":[66,145,171],"moment":[67,105],"base":[68,106],"functions":[69,107],"orders":[72,152],"having":[73],"number":[75],"zero-crossings":[77],"very":[79,95],"shapes,":[81],"therefore":[82],"they":[83,112],"can":[84],"better":[85],"separate":[86,153],"features":[88,172],"based":[89],"modes,":[92],"which":[93,193],"is":[94,160,183,188],"interesting":[96],"for":[97],"shape":[101],"classification.":[102],"Moreover,":[103],"much":[109],"more":[110,157],"smoothed,":[111],"thus":[114],"less":[115],"sensitive":[116],"noise":[118],"avoid":[120],"artifacts":[122],"introduced":[123],"by":[124,190],"window":[125],"function":[126],"discontinuity.":[127],"We":[128],"then":[129,195],"spectral":[132],"frequency":[137,155],"Theoretical":[139],"numerical":[141,191],"analyses":[142],"show":[143],"that":[144,163],"Legendre":[146],"bands":[156],"effectively.":[158],"It":[159],"also":[161,184],"shown":[162],"approach":[168],"construct":[170],"from":[173],"results":[175],"wavelet":[177],"The":[179],"orthogonality":[180],"equivalence":[181],"theorem":[182],"presented.":[185],"confirmed":[189],"results,":[192],"reported.":[196]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}