{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:25:25Z","timestamp":1763468725011,"version":"3.40.5"},"reference-count":48,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T00:00:00Z","timestamp":1638057600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["81870815","82071171"],"award-info":[{"award-number":["81870815","82071171"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Anatomy"],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The three\u2010dimensional (3D) symmetry reference plane (SRP) is the premise and basis of 3D facial symmetry analysis. Currently, most methods for extracting the SRP are based on anatomical landmarks measured manually using a digital 3D facial model. However, as different clinicians have varying definitions of landmarks, establishing common methods suitable for different types of facial asymmetry remains challenging. The present study aimed to investigate and evaluate a novel mathematical algorithm based on power function weighted Procrustes analysis (PWPA) to determine 3D facial SRPs for patients with mandibular deviation. From 30 patients with mandibular deviation, 3D facial SRPs were determined using both our PWPA algorithms (two functions) and the traditional PA algorithm (experimental groups). A reference plane, defined by experts, was considered the \u2018truth plane\u2019. The \u2018position error\u2019 index of mirrored landmarks was created to quantitatively evaluate the difference among the PWPA SRPs and the truth plane, including overall differences and regional differences of the face (upper, middle and lower). The \u2018angle error\u2019 values between the SRPs and the truth plane in the experimental groups were also evaluated in this study. Statistics and measurement analyses were used to comprehensively evaluate the clinical suitability of the PWPA algorithms to construct the SRP. The average angle error values between the PWPA SRPs of the two functions and the truth plane were 1.21\u00a0\u00b1\u00a00.65\u00b0 and 1.18\u00a0\u00b1\u00a00.62\u00b0, which were smaller than those between the PA SRP and the truth plane. The position error values of mirrored landmarks constructed using the PWPA algorithms for the whole face and for each facial partition were lower than those constructed using the PA algorithm. In conclusion, for patients with mandibular deviation, this novel mathematical algorithm provided a more suitable SRP for their 3D facial model, which achieved a result approaching the true effect of experts.<\/jats:p>","DOI":"10.1111\/joa.13564","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T05:30:27Z","timestamp":1638163827000},"page":"556-566","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A mathematical algorithm of the facial symmetry plane: Application to mandibular deformity 3D facial data"],"prefix":"10.1111","volume":"240","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9234-5783","authenticated-orcid":false,"given":"Yujia","family":"Zhu","sequence":"first","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangling","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Computer Science Beijing University of Posts and Telecommunications (National Pilot Software Engineering School)  Beijing PR China"},{"name":"Key Laboratory of Trustworthy Distributed Computing and Service Ministry of Education Beijing University of Posts and Telecommunications  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengwen","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Computer Science Beijing University of Posts and Telecommunications (National Pilot Software Engineering School)  Beijing PR China"},{"name":"Key Laboratory of Trustworthy Distributed Computing and Service Ministry of Education Beijing University of Posts and Telecommunications  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aonan","family":"Wen","sequence":"additional","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Xiao","sequence":"additional","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yijiao","family":"Zhao","sequence":"additional","affiliation":[{"name":"Center of Digital Dentistry\/Department of Prosthodontics Peking University School and Hospital of Stomatology  Beijing PR China"},{"name":"National Center of Stomatology  Beijing PR China"},{"name":"National Clinical Research Center for Oral Diseases  Beijing PR China"},{"name":"National Engineering Laboratory for Digital and Material Technology of Stomatology  Beijing PR China"},{"name":"Beijing Key Laboratory of Digital Stomatology  Beijing PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,11,28]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2017.08.007"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bjps.2018.10.004"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1177\/1055665618780108"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1515\/bmt-2014-0024"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.121791"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0262-8856(92)90066-C"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2011.10.019"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-7580.2012.01528.x"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-7580.2011.01411.x"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00784-011-0512-4"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2006.01.028"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/ejo\/cjr091"},{"key":"e_1_2_12_14_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0188039"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2675341"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2015.11.013"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1037\/0735-7036.108.3.233"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.2319\/022107-85.1"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00056-007-0652-y"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00056-005-0445-0"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00056-007-0604-6"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/ocr.12010"},{"key":"e_1_2_12_23_1","doi-asserted-by":"publisher","DOI":"10.4041\/kjod.2012.42.2.56"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.5624\/isd.2015.45.4.227"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.2319\/112112-890.1"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajodo.2008.08.029"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11692-009-9061-z"},{"key":"e_1_2_12_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2713940"},{"key":"e_1_2_12_29_1","first-page":"215","article-title":"3D dentofacial photogrammetry reference values: a novel approach to orthodontic diagnosis","volume":"39","author":"Masoud M.I.","year":"2016","journal-title":"European Journal of Orthodontics"},{"key":"e_1_2_12_30_1","doi-asserted-by":"publisher","DOI":"10.1037\/0022-3514.76.1.151"},{"key":"e_1_2_12_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.archoralbio.2014.08.004"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1097\/00006534-199909040-00006"},{"key":"e_1_2_12_33_1","doi-asserted-by":"publisher","DOI":"10.1093\/ejo\/cjq146"},{"key":"e_1_2_12_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2008.12.009"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/1096-8628(20000717)93:2<143::AID-AJMG12>3.0.CO;2-Q"},{"key":"e_1_2_12_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2003.819276"},{"key":"e_1_2_12_37_1","first-page":"203","article-title":"An approach to extraction midsagittal plane of skull from brain CT images for oral and maxillofacial surgery","volume":"7","author":"Tan W.","year":"2019","journal-title":"IEEE Access"},{"key":"e_1_2_12_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40484-016-0086-x"},{"key":"e_1_2_12_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2012.05.036"},{"key":"e_1_2_12_40_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0059391"},{"key":"e_1_2_12_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcms.2016.07.017"},{"key":"e_1_2_12_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijom.2012.05.021"},{"key":"e_1_2_12_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.medengphy.2013.06.006"},{"key":"e_1_2_12_44_1","doi-asserted-by":"publisher","DOI":"10.1597\/15-053"},{"key":"e_1_2_12_45_1","doi-asserted-by":"publisher","DOI":"10.1097\/SCS.0000000000002376"},{"key":"e_1_2_12_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bandc.2004.08.056"},{"key":"e_1_2_12_47_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207450590914464"},{"key":"e_1_2_12_48_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2784571"},{"key":"e_1_2_12_49_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12903-020-01311-3"}],"container-title":["Journal of Anatomy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/joa.13564","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/joa.13564","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/joa.13564","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T10:43:45Z","timestamp":1693219425000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/joa.13564"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,28]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["10.1111\/joa.13564"],"URL":"https:\/\/doi.org\/10.1111\/joa.13564","archive":["Portico"],"relation":{},"ISSN":["0021-8782","1469-7580"],"issn-type":[{"type":"print","value":"0021-8782"},{"type":"electronic","value":"1469-7580"}],"subject":[],"published":{"date-parts":[[2021,11,28]]},"assertion":[{"value":"2021-07-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-09-24","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-11-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}