{"id":"https://openalex.org/W2099474155","doi":"https://doi.org/10.1109/tip.2011.2173206","title":"On the Mathematical Properties of the Structural Similarity Index","display_name":"On the Mathematical Properties of the Structural Similarity Index","publication_year":2011,"publication_date":"2011-10-25","ids":{"openalex":"https://openalex.org/W2099474155","doi":"https://doi.org/10.1109/tip.2011.2173206","mag":"2099474155","pmid":"https://pubmed.ncbi.nlm.nih.gov/22042163"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2011.2173206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2173206","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/A5115069267","display_name":"Dominique Brunet","orcid":"https://orcid.org/0000-0002-5725-0866"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. Brunet","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada. dbrunet@uwaterloo.ca","Dept. of Appl. Math- ematics, Univ. of WaterlooWaterloo, Waterloo, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada. dbrunet@uwaterloo.ca","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Dept. of Appl. Math- ematics, Univ. of WaterlooWaterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077444272","display_name":"Edward R. Vrscay","orcid":"https://orcid.org/0000-0001-9158-5910"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"E. R. Vrscay","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","Dept. of Appl. Math- ematics, Univ. of WaterlooWaterloo, Waterloo, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Dept. of Appl. Math- ematics, Univ. of WaterlooWaterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100420313","display_name":"Zhou Wang","orcid":"https://orcid.org/0000-0003-4413-4441"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhou Wang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ONT, Canada","[Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada]","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.5023,"has_fulltext":false,"cited_by_count":586,"citation_normalized_percentile":{"value":0.9944802,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"21","issue":"4","first_page":"1488","last_page":"1499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"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/T11165","display_name":"Image and Video Quality Assessment","score":0.9970999956130981,"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/T11605","display_name":"Visual Attention and Saliency Detection","score":0.996399998664856,"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/convexity","display_name":"Convexity","score":0.8123564720153809},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5847494602203369},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.547374963760376},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.5447635650634766},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5309616327285767},{"id":"https://openalex.org/keywords/image-quality","display_name":"Image quality","score":0.4479762613773346},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.442262202501297},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.43656620383262634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43206363916397095},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"Triangle inequality","score":0.42546698451042175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4204794466495514},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.40048763155937195},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39606428146362305},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3408748507499695},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.32686561346054077},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.26954618096351624},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18686649203300476},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1339404284954071}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8123564720153809},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5847494602203369},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.547374963760376},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.5447635650634766},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5309616327285767},{"id":"https://openalex.org/C55020928","wikidata":"https://www.wikidata.org/wiki/Q3813865","display_name":"Image quality","level":3,"score":0.4479762613773346},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.442262202501297},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.43656620383262634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43206363916397095},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.42546698451042175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4204794466495514},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.40048763155937195},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39606428146362305},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3408748507499695},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.32686561346054077},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.26954618096351624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18686649203300476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1339404284954071},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2011.2173206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2173206","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:22042163","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22042163","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},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.705.6991","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.705.6991","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ece.uwaterloo.ca/%7Ez70wang/publications/TIP_SSIM_MathProperties.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1580389772","https://openalex.org/W1862916997","https://openalex.org/W1970642807","https://openalex.org/W1972348417","https://openalex.org/W1973207880","https://openalex.org/W1996062483","https://openalex.org/W2009272644","https://openalex.org/W2009707700","https://openalex.org/W2025409544","https://openalex.org/W2028276782","https://openalex.org/W2039939082","https://openalex.org/W2046119925","https://openalex.org/W2081003258","https://openalex.org/W2085518012","https://openalex.org/W2088836904","https://openalex.org/W2090462163","https://openalex.org/W2092591518","https://openalex.org/W2099799750","https://openalex.org/W2103232506","https://openalex.org/W2109761230","https://openalex.org/W2114549779","https://openalex.org/W2114582993","https://openalex.org/W2115141424","https://openalex.org/W2115838129","https://openalex.org/W2126226185","https://openalex.org/W2130815094","https://openalex.org/W2133665775","https://openalex.org/W2134227958","https://openalex.org/W2136227079","https://openalex.org/W2137136191","https://openalex.org/W2141983208","https://openalex.org/W2143214446","https://openalex.org/W2143612128","https://openalex.org/W2144221002","https://openalex.org/W2146411623","https://openalex.org/W2158003722","https://openalex.org/W2159269332","https://openalex.org/W2159372562","https://openalex.org/W2160046865","https://openalex.org/W2171349048","https://openalex.org/W2296319761","https://openalex.org/W2327468149","https://openalex.org/W2611537933","https://openalex.org/W2626610348","https://openalex.org/W2994790045","https://openalex.org/W3100937421","https://openalex.org/W4211253871","https://openalex.org/W4233514353","https://openalex.org/W4238799204","https://openalex.org/W4250589301","https://openalex.org/W6649218010","https://openalex.org/W6679984885"],"related_works":["https://openalex.org/W2187391117","https://openalex.org/W2056357792","https://openalex.org/W1981809986","https://openalex.org/W1843467136","https://openalex.org/W2949367465","https://openalex.org/W2051545453","https://openalex.org/W2006359264","https://openalex.org/W3029201158","https://openalex.org/W4299607453","https://openalex.org/W2186138725"],"abstract_inverted_index":{"Since":[0],"its":[1],"introduction":[2],"in":[3,48,51,175],"2004,":[4],"the":[5,19,26,65,71,76,80,99,122,145,156,171],"structural":[6],"similarity":[7],"(SSIM)":[8],"index":[9],"has":[10,35],"gained":[11],"widespread":[12],"popularity":[13],"as":[14,44,90],"a":[15,38,52,112,151],"tool":[16],"to":[17,24],"assess":[18],"quality":[20],"of":[21,28,41,54,67,73,75,79,114,125,153,173],"images":[22],"and":[23,32,92,116,138,158,179],"evaluate":[25],"performance":[27],"image":[29,55],"processing":[30,56],"algorithms":[31],"systems.":[33],"There":[34],"been":[36],"also":[37],"growing":[39],"interest":[40],"using":[42],"SSIM":[43,81,174],"an":[45],"objective":[46],"function":[47],"optimization":[49],"problems":[50],"variety":[53],"applications.":[57,181],"One":[58],"major":[59],"issue":[60],"that":[61,95,130],"could":[62],"strongly":[63],"impede":[64],"progress":[66],"such":[68,89,131],"efforts":[69],"is":[70],"lack":[72],"understanding":[74],"mathematical":[77],"properties":[78,88],"measure.":[82],"For":[83],"example,":[84],"some":[85],"highly":[86],"desirable":[87],"convexity":[91,154],"triangular":[93],"inequality":[94],"are":[96,134],"possessed":[97],"by":[98],"mean":[100],"squared":[101],"error":[102],"may":[103],"not":[104],"hold.":[105],"In":[106],"this":[107],"paper,":[108],"we":[109],"first":[110],"construct":[111],"series":[113],"normalized":[115],"generalized":[117],"(vector-valued)":[118],"metrics":[119,137],"based":[120],"on":[121],"important":[123],"ingredients":[124],"SSIM.":[126],"We":[127],"then":[128],"show":[129],"modified":[132],"measures":[133],"valid":[135],"distance":[136,159],"have":[139],"many":[140],"useful":[141],"properties,":[142],"among":[143],"which":[144],"most":[146],"significant":[147],"ones":[148],"include":[149],"quasi-convexity,":[150],"region":[152],"around":[155],"minimizer,":[157],"preservation":[160],"under":[161],"orthogonal":[162],"or":[163],"unitary":[164],"transformations.":[165],"The":[166],"groundwork":[167],"laid":[168],"here":[169],"extends":[170],"potentials":[172],"both":[176],"theoretical":[177],"development":[178],"practical":[180]},"counts_by_year":[{"year":2026,"cited_by_count":37},{"year":2025,"cited_by_count":96},{"year":2024,"cited_by_count":78},{"year":2023,"cited_by_count":62},{"year":2022,"cited_by_count":60},{"year":2021,"cited_by_count":55},{"year":2020,"cited_by_count":42},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2025-10-10T00:00:00"}