A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm
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RESEARCH ARTICLE
Open Access
A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm Yujia Zhu1,2,3,4,5, Shengwen Zheng6,7, Guosheng Yang6,7, Xiangling Fu6,7, Ning Xiao1,2,3,4,5, Aonan Wen1,2,3,4,5, Yong Wang1,2,3,4,5* and Yijiao Zhao1,2,3,4,5*
Abstract Background: We aimed to establish a novel method, using the weighted Procrustes analysis (WPA) algorithm, which assigns weight to facial anatomical landmarks, to construct a three-dimensional facial symmetry reference plane (SRP) for mandibular deviation patients. Methods: Three-dimensional facial SRPs were independently extracted from 15 mandibular deviation patients using both our WPA algorithm and the standard PA algorithm. A reference plane was defined to serve as the ground truth. To determine whether the WPA SRP or the PA SRP was closer to the ground truth, we measured the position error of mirrored landmarks, the facial asymmetry index (FAI) error, and the angle error for the global face and each facial third partition. Results: The average angle error between the WPA SRP and the ground truth was 1.66 ± 0.81°, which was smaller than that between the PA SRP and the ground truth. The position error of the mirrored landmarks constructed using the WPA algorithm in the global face (3.64 ± 1.53 mm) and each facial partition was lower than that constructed using the PA algorithm. The average FAI error of the WPA SRP was − 7.77 ± 17.02 mm, which was smaller than that of the PA SRP. Conclusions: This novel automatic algorithm, based on weighted anatomic landmarks, can provide a more adaptable SRP than the standard PA algorithm when applied to severe mandibular deviation patients and can better simulate the diagnosis strategies of clinical experts. Keywords: Symmetry reference plane, Procrustes analysis, Three-dimensional facial data, Mandibular deviation, Anatomic landmarks Background Mandibular deviation is one of the more common manifestations of facial asymmetry, accounting for 70–80% of all cases [1–3]. The restoration of symmetrical, coordinated, and aesthetic facial shapes is a central focus of oral *Correspondence: [email protected]; [email protected] 1 Center of Digital Dentistry, Peking University School and Hospital of Stomatology, No.22 Zhongguancun Avenue South, Haidian District, Beijing 100081, China Full list of author information is available at the end of the article
and maxillofacial surgery, orthodontics and prosthodontics [4–6]. Using three-dimensional digital technology, the extraction of the symmetry reference plane (SRP) is the primary step during symmetry analysis of threedimensional facial data [7]. SRP accuracy directly affects the symmetry index and is critical for developing treatment strategies and evaluating treatment progress. The traditional methods for extracting an SRP are often based on medical and bilateral anatomical landmarks measured either using a digital three-dimensional facial model or having the head in a natural position [8–11].
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