{"id":"https://openalex.org/W2094273709","doi":"https://doi.org/10.1109/tip.2014.2365353","title":"General Form for Obtaining Unit Disc-Based Generalized Orthogonal Moments","display_name":"General Form for Obtaining Unit Disc-Based Generalized Orthogonal Moments","publication_year":2014,"publication_date":"2014-10-27","ids":{"openalex":"https://openalex.org/W2094273709","doi":"https://doi.org/10.1109/tip.2014.2365353","mag":"2094273709","pmid":"https://pubmed.ncbi.nlm.nih.gov/25361505"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2014.2365353","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2014.2365353","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5005274186","display_name":"Hongqing Zhu","orcid":"https://orcid.org/0000-0002-2122-7066"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongqing Zhu","raw_affiliation_strings":["School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","School of information Science and Engineering, East China University of Science and Technology, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"School of information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101785882","display_name":"Yan Yang","orcid":"https://orcid.org/0000-0003-4794-2313"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Yang","raw_affiliation_strings":["School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","School of information Science and Engineering, East China University of Science and Technology, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"School of information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004537111","display_name":"Xiaoli Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoli Zhu","raw_affiliation_strings":["School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","School of information Science and Engineering, East China University of Science and Technology, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"School of information Science and Engineering, East China University of Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075478974","display_name":"Zhiguo Gui","orcid":"https://orcid.org/0000-0002-8991-9907"},"institutions":[{"id":"https://openalex.org/I135714990","display_name":"North University of China","ror":"https://ror.org/047bp1713","country_code":"CN","type":"education","lineage":["https://openalex.org/I135714990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiguo Gui","raw_affiliation_strings":["National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, China","[National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, China]"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, China","institution_ids":["https://openalex.org/I135714990"]},{"raw_affiliation_string":"[National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, China]","institution_ids":["https://openalex.org/I135714990"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100687822","display_name":"Huazhong Shu","orcid":"https://orcid.org/0000-0002-3833-7915"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huazhong Shu","raw_affiliation_strings":["School of Computer Science and Engineering, Southeast University, Nanjing, China","[School of Computer Science & Engineering, Southeast University, Nanjing, China]"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"[School of Computer Science & Engineering, Southeast University, Nanjing, China]","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005274186"],"corresponding_institution_ids":["https://openalex.org/I143593769"],"apc_list":null,"apc_paid":null,"fwci":0.4877,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.7071271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"12","first_page":"5455","last_page":"5469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9866999983787537,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.963100016117096,"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/zernike-polynomials","display_name":"Zernike polynomials","score":0.8189854621887207},{"id":"https://openalex.org/keywords/velocity-moments","display_name":"Velocity Moments","score":0.8162984848022461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6985722780227661},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6364261507987976},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.617795467376709},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.5937300324440002},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5593100190162659},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5270217657089233},{"id":"https://openalex.org/keywords/orthogonal-functions","display_name":"Orthogonal functions","score":0.4620133936405182},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4572860598564148},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.4469369053840637},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43690356612205505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4293391704559326},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3921167850494385},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2478111982345581},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1457340121269226}],"concepts":[{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.8189854621887207},{"id":"https://openalex.org/C149539972","wikidata":"https://www.wikidata.org/wiki/Q7919290","display_name":"Velocity Moments","level":4,"score":0.8162984848022461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6985722780227661},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6364261507987976},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.617795467376709},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.5937300324440002},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5593100190162659},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5270217657089233},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.4620133936405182},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4572860598564148},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.4469369053840637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43690356612205505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4293391704559326},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3921167850494385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2478111982345581},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1457340121269226},{"id":"https://openalex.org/C165699331","wikidata":"https://www.wikidata.org/wiki/Q461533","display_name":"Wavefront","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2014.2365353","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2014.2365353","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:25361505","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25361505","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G106592211","display_name":null,"funder_award_id":"61271357","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2784902399","display_name":null,"funder_award_id":"2011CB707904","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4621034529","display_name":null,"funder_award_id":"61271312","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6312289913","display_name":null,"funder_award_id":"61371150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W131298322","https://openalex.org/W358380361","https://openalex.org/W1503169376","https://openalex.org/W1980472188","https://openalex.org/W2003065196","https://openalex.org/W2004082669","https://openalex.org/W2011974067","https://openalex.org/W2025689743","https://openalex.org/W2059176986","https://openalex.org/W2063557866","https://openalex.org/W2069455443","https://openalex.org/W2075260191","https://openalex.org/W2086936614","https://openalex.org/W2089042189","https://openalex.org/W2102238397","https://openalex.org/W2121761475","https://openalex.org/W2121834080","https://openalex.org/W2124041826","https://openalex.org/W2135331233","https://openalex.org/W2141381332","https://openalex.org/W2144581836","https://openalex.org/W2146880335","https://openalex.org/W2159005573","https://openalex.org/W2169013230","https://openalex.org/W2539912226","https://openalex.org/W2613361586","https://openalex.org/W6605386981","https://openalex.org/W6629916440","https://openalex.org/W6728850812","https://openalex.org/W6737704252"],"related_works":["https://openalex.org/W2372021815","https://openalex.org/W2360964508","https://openalex.org/W2122970665","https://openalex.org/W1596812724","https://openalex.org/W2086936614","https://openalex.org/W4321260167","https://openalex.org/W2765956955","https://openalex.org/W2141381332","https://openalex.org/W2168501771","https://openalex.org/W2619709459"],"abstract_inverted_index":{"The":[0,112,135],"rotation":[1,179],"invariance":[2],"of":[3,28,40,56,105,114,122,146,161,198,224],"the":[4,26,38,65,153,189,196,205,212,218],"classical":[5,136,219],"disc-based":[6,57,220],"moments,":[7],"such":[8,175],"as":[9,23,98,176],"Zernike":[10],"moments":[11,18,110,150,221],"(ZMs),":[12],"pseudo-ZMs":[13],"(PZMs),":[14],"and":[15,77,131,139,172,178,192,228],"orthogonal":[16,63,109,123],"Fourier-Mellin":[17],"(OFMMs),":[19],"makes":[20],"them":[21],"attractive":[22],"descriptors":[24],"for":[25,37,83,151,169,195],"purpose":[27],"recognition":[29,173],"tasks.":[30],"However,":[31],"less":[32],"work":[33],"has":[34],"been":[35],"performed":[36],"generalization":[39],"these":[41,92,147,199],"moment":[42],"functions.":[43],"In":[44,181],"this":[45,162],"paper,":[46],"four":[47],"general":[48],"forms":[49],"are":[50,62,71,81,96,215],"developed":[51,186],"to":[52,73,101,142,203,217],"obtain":[53],"a":[54,103,143],"class":[55],"generalized":[58,108,126,129,133,149],"radial":[59,69,94,201],"polynomials":[60,70,95,202],"that":[61,211],"over":[64],"unit":[66,106],"circle.":[67],"These":[68],"scaled":[72,93],"ensure":[74],"numerical":[75,206],"stability,":[76],"some":[78,166],"useful":[79],"properties":[80,168],"discussed":[82],"potential":[84],"applications":[85],"they":[86],"could":[87],"be":[88],"used":[89,97],"in.":[90],"Then,":[91],"kernel":[99],"functions":[100],"construct":[102],"series":[104],"discbased":[107],"(DGMs).":[111],"variation":[113],"parameters":[115],"in":[116,222],"DGMs":[117],"can":[118],"form":[119],"various":[120],"types":[121],"moments:":[124],"1)":[125],"ZMs;":[127],"2)":[128],"PZMs;":[130],"3)":[132],"OFMMs.":[134],"ZMs,":[137],"PZMs,":[138],"OFMMs":[140],"correspond":[141],"special":[144],"case":[145],"three":[148],"which":[152],"free":[154],"parameter":[155],"\u03b1":[156],"=":[157],"0.":[158],"Each":[159],"member":[160],"family":[163],"will":[164],"share":[165],"excellent":[167],"image":[170,225],"representation":[171,226],"tasks,":[174],"orthogonality":[177],"invariance.":[180],"addition,":[182],"we":[183],"have":[184],"also":[185],"two":[187],"algorithms,":[188],"so-called":[190],"m-recursive":[191],"n-recursive":[193],"methods":[194,214],"computation":[197],"proposed":[200,213],"improve":[204],"stability.":[207],"Experimental":[208],"results":[209],"show":[210],"superior":[216],"terms":[223],"capability":[227],"classification":[229],"accuracy.":[230]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}