{"id":"https://openalex.org/W4207039940","doi":"https://doi.org/10.1109/tim.2022.3145361","title":"Nonlinear Correction for Fringe Projection Profilometry With Shifted-Phase Histogram Equalization","display_name":"Nonlinear Correction for Fringe Projection Profilometry With Shifted-Phase Histogram Equalization","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4207039940","doi":"https://doi.org/10.1109/tim.2022.3145361"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2022.3145361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2022.3145361","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","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/A5100402336","display_name":"Yuwei Wang","orcid":"https://orcid.org/0000-0003-4282-9821"},"institutions":[{"id":"https://openalex.org/I140221134","display_name":"Anhui Agricultural University","ror":"https://ror.org/0327f3359","country_code":"CN","type":"education","lineage":["https://openalex.org/I140221134"]},{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuwei Wang","raw_affiliation_strings":["College of Engineering, Anhui Agricultural University, Hefei, China","Department of Opto-Electronics, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-4282-9821","affiliations":[{"raw_affiliation_string":"College of Engineering, Anhui Agricultural University, Hefei, China","institution_ids":["https://openalex.org/I140221134"]},{"raw_affiliation_string":"Department of Opto-Electronics, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016167521","display_name":"Jiaxu Cai","orcid":"https://orcid.org/0000-0002-8080-1902"},"institutions":[{"id":"https://openalex.org/I140221134","display_name":"Anhui Agricultural University","ror":"https://ror.org/0327f3359","country_code":"CN","type":"education","lineage":["https://openalex.org/I140221134"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaxu Cai","raw_affiliation_strings":["College of Engineering, Anhui Agricultural University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-8080-1902","affiliations":[{"raw_affiliation_string":"College of Engineering, Anhui Agricultural University, Hefei, China","institution_ids":["https://openalex.org/I140221134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032085236","display_name":"Dashan Zhang","orcid":"https://orcid.org/0000-0002-2416-1058"},"institutions":[{"id":"https://openalex.org/I140221134","display_name":"Anhui Agricultural University","ror":"https://ror.org/0327f3359","country_code":"CN","type":"education","lineage":["https://openalex.org/I140221134"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dashan Zhang","raw_affiliation_strings":["College of Engineering, Anhui Agricultural University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-2416-1058","affiliations":[{"raw_affiliation_string":"College of Engineering, Anhui Agricultural University, Hefei, China","institution_ids":["https://openalex.org/I140221134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076522066","display_name":"Xiangcheng Chen","orcid":"https://orcid.org/0000-0002-3403-7675"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangcheng Chen","raw_affiliation_strings":["School of Artificial Intelligence, Anhui University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-3403-7675","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100454881","display_name":"Yajun Wang","orcid":"https://orcid.org/0000-0002-0165-0561"},"institutions":[{"id":"https://openalex.org/I140221134","display_name":"Anhui Agricultural University","ror":"https://ror.org/0327f3359","country_code":"CN","type":"education","lineage":["https://openalex.org/I140221134"]},{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yajun Wang","raw_affiliation_strings":["College of Engineering, Anhui Agricultural University, Hefei, China","Department of Opto-Electronics, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-0165-0561","affiliations":[{"raw_affiliation_string":"College of Engineering, Anhui Agricultural University, Hefei, China","institution_ids":["https://openalex.org/I140221134"]},{"raw_affiliation_string":"Department of Opto-Electronics, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3067,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.95551206,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"71","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":1.0,"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/T10638","display_name":"Optical measurement and interference techniques","score":1.0,"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/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T14158","display_name":"Optical Systems and Laser Technology","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/histogram","display_name":"Histogram","score":0.8299590349197388},{"id":"https://openalex.org/keywords/histogram-matching","display_name":"Histogram matching","score":0.8018246293067932},{"id":"https://openalex.org/keywords/histogram-equalization","display_name":"Histogram equalization","score":0.7429442405700684},{"id":"https://openalex.org/keywords/adaptive-histogram-equalization","display_name":"Adaptive histogram equalization","score":0.683975100517273},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.5559270977973938},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5189464092254639},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49711278080940247},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4668598473072052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46159717440605164},{"id":"https://openalex.org/keywords/equalization","display_name":"Equalization (audio)","score":0.43942970037460327},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4332396984100342},{"id":"https://openalex.org/keywords/color-normalization","display_name":"Color normalization","score":0.4157436490058899},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37740734219551086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3580836057662964},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.15540775656700134},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.15206798911094666},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12406450510025024}],"concepts":[{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.8299590349197388},{"id":"https://openalex.org/C127449775","wikidata":"https://www.wikidata.org/wiki/Q3785871","display_name":"Histogram matching","level":4,"score":0.8018246293067932},{"id":"https://openalex.org/C136943445","wikidata":"https://www.wikidata.org/wiki/Q1970240","display_name":"Histogram equalization","level":4,"score":0.7429442405700684},{"id":"https://openalex.org/C30387639","wikidata":"https://www.wikidata.org/wiki/Q4680744","display_name":"Adaptive histogram equalization","level":5,"score":0.683975100517273},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5559270977973938},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5189464092254639},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49711278080940247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4668598473072052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46159717440605164},{"id":"https://openalex.org/C75755367","wikidata":"https://www.wikidata.org/wiki/Q104531076","display_name":"Equalization (audio)","level":3,"score":0.43942970037460327},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4332396984100342},{"id":"https://openalex.org/C44404184","wikidata":"https://www.wikidata.org/wiki/Q5148620","display_name":"Color normalization","level":5,"score":0.4157436490058899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37740734219551086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3580836057662964},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.15540775656700134},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.15206798911094666},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12406450510025024},{"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C142616399","wikidata":"https://www.wikidata.org/wiki/Q5148604","display_name":"Color image","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tim.2022.3145361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2022.3145361","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3835222437","display_name":null,"funder_award_id":"51805006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5210192005","display_name":null,"funder_award_id":"51905005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5962989989","display_name":null,"funder_award_id":"2008085QF318","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1969106758","https://openalex.org/W1981579689","https://openalex.org/W2005389892","https://openalex.org/W2008239695","https://openalex.org/W2048747197","https://openalex.org/W2087256761","https://openalex.org/W2093951181","https://openalex.org/W2112248265","https://openalex.org/W2135114731","https://openalex.org/W2154784878","https://openalex.org/W2441234261","https://openalex.org/W2695315630","https://openalex.org/W2762962995","https://openalex.org/W2789248836","https://openalex.org/W2801729002","https://openalex.org/W2804654620","https://openalex.org/W2808086381","https://openalex.org/W2965283655","https://openalex.org/W2980525487","https://openalex.org/W2999117695","https://openalex.org/W3015821893","https://openalex.org/W3033101048","https://openalex.org/W3041814977","https://openalex.org/W3118237753","https://openalex.org/W3120661620","https://openalex.org/W3130247572","https://openalex.org/W3130295290","https://openalex.org/W3193545624"],"related_works":["https://openalex.org/W2170563037","https://openalex.org/W2387482914","https://openalex.org/W2162593906","https://openalex.org/W2015245117","https://openalex.org/W2354812287","https://openalex.org/W1597132678","https://openalex.org/W2385217229","https://openalex.org/W2396115542","https://openalex.org/W2912390010","https://openalex.org/W2266849835"],"abstract_inverted_index":{"Fringe":[0],"projection":[1],"profilometry":[2],"has":[3],"been":[4,198],"widely":[5],"used":[6],"for":[7,62],"3-D":[8],"measurement,":[9],"but":[10,27],"the":[11,16,19,22,30,44,67,70,82,95,100,104,118,124,142,147,150,158,167,172,187,206,213,221,228],"gamma":[12],"nonlinearity":[13],"severely":[14],"affects":[15],"accuracy.":[17],"Ideally,":[18],"histogram":[20,46,58,72,102,140,148,164,192,216],"of":[21,29,126,149,157],"undistorted":[23,159,173],"phase":[24,32,45,84,152,169,215],"is":[25],"uniform,":[26],"that":[28,69,156,205],"distorted":[31,71,151,168],"becomes":[33],"nonuniform.":[34],"In":[35],"practice,":[36],"adequate":[37],"sampling":[38,127],"pixels":[39,128],"are":[40],"required":[41],"to":[42,170,185],"calculate":[43],"from":[47],"modulated":[48],"fringe":[49],"patterns.":[50],"Therefore,":[51],"this":[52,176],"article":[53,177],"proposes":[54,178],"an":[55],"effective":[56],"shifted-phase":[57],"equalization":[59,165,217],"(SHE)":[60],"method":[61,184,209,224],"nonlinear":[63],"correction.":[64],"Based":[65],"on":[66,166],"finding":[68],"contains":[73],"three":[74,132],"symmetric":[75],"valleys":[76],"in":[77],"theory,":[78],"if":[79],"we":[80,110,135,161],"shift":[81],"wrapped":[83],"by":[85,131,191],"<inline-formula":[86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[88],"<tex-math":[89],"notation=\"LaTeX\">$\\pm":[90],"2\\pi":[91],"$":[92],"</tex-math></inline-formula>":[93],"/3,":[94],"shifted":[96,115,122],"phases":[97],"will":[98,129],"share":[99],"same":[101],"as":[103,155],"original":[105,119,143],"phase.":[106,144,174],"Without":[107],"additional":[108],"patterns,":[109],"can":[111,136,225],"easily":[112],"obtain":[113,137],"two":[114,121],"phases.":[116],"Combining":[117],"and":[120,134,195,201,220],"phases,":[123],"number":[125],"increase":[130],"times,":[133],"more":[138],"accurate":[139],"than":[141,212],"To":[145],"make":[146],"be":[153],"uniform":[154],"phase,":[160],"directly":[162],"apply":[163],"estimate":[171],"Moreover,":[175],"a":[179],"spline":[180],"interpolation":[181],"optimization":[182],"(SIO)":[183],"eliminate":[186],"discretization":[188,229],"error":[189],"caused":[190],"equalization.":[193],"Simulations":[194],"experiments":[196],"have":[197],"carried":[199],"out,":[200],"their":[202],"results":[203],"indicate":[204],"proposed":[207,222],"SHE":[208],"performs":[210],"better":[211],"conventional":[214],"(PHE)":[218],"method,":[219],"SIO":[223],"further":[226],"reduce":[227],"error.":[230]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}