{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:04:46Z","timestamp":1760148286351,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T00:00:00Z","timestamp":1681776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"HKRGC GRF","award":["14306721","2130772"],"award-info":[{"award-number":["14306721","2130772"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We address the problem of craniofacial morphometric analysis using geometric models, which has important clinical applications for the diagnosis of syndromes associated with craniofacial dysmorphologies. In this work, a novel geometric model is proposed to analyze craniofacial structures based on local curvature information and Teichm\u00fcller mappings. A key feature of the proposed model is that its pipeline starts with few two-dimensional images of the human face captured at different angles, from which the three-dimensional craniofacial structure can be reconstructed. The 3D surface reconstruction from 2D images is based on a modified 3D morphable model (3DMM) framework. Geometric quantities around important feature landmarks according to different clinical applications can then be computed on each three-dimensional craniofacial structure. Together with the Teichm\u00fcller mapping, the landmark-based Teichm\u00fcller curvature distances (LTCDs) for every classes can be computed, which are further used for three-class classification. A composite score model is used and the parameter optimization is carried out to further improve the classification accuracy. Our proposed model is applied to study the craniofacial structures of children with and without the obstructive sleep apnoea (OSA). Sixty subjects, with accessible multi-angle photography and polysomnography (PSG) data, are divided into three classes based on the severity of OSA. Using our proposed model, our proposed model achieves a high 90% accuracy, which outperforms other existing models. This demonstrates the effectiveness of our proposed geometric model for craniofacial analysis.<\/jats:p>","DOI":"10.3390\/axioms12040393","type":"journal-article","created":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T01:39:05Z","timestamp":1681868345000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Quasiconformal-Based Geometric Model for Craniofacial Analysis and Its Application"],"prefix":"10.3390","volume":"12","author":[{"given":"Ming-Hei","family":"Wong","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meixi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"King-Man","family":"Tam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hoi-Man","family":"Yuen","sequence":"additional","affiliation":[{"name":"Department of Paediatrics, Prince of Wales Hospital, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun-Ting","family":"Au","sequence":"additional","affiliation":[{"name":"Department of Paediatrics, Prince of Wales Hospital, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7272-8285","authenticated-orcid":false,"given":"Kate Ching-Ching","family":"Chan","sequence":"additional","affiliation":[{"name":"Department of Paediatrics, Prince of Wales Hospital, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Albert Martin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Paediatrics, Prince of Wales Hospital, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lok-Ming","family":"Lui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.5664\/jcsm.7518","article-title":"Potential anatomic markers of obstructive sleep apnea in prepubertal children","volume":"14","author":"Au","year":"2018","journal-title":"J. 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