ArticleJournal of anatomy2022
A mathematical algorithm of the facial symmetry plane: Application to mandibular deformity 3D facial data.
Article in Journal of anatomy, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed, 10 citations in OpenAlex.
- 3D Photogrammetry-Driven Craniofacial Analysis in Orthodontics: A Scoping Review of Recent Applications.Bioengineering (Basel, Switzerland) · 2025Review
- Review
- Comparison of Mirroring and Overlapping Analysis and Three-Dimensional Soft Tissue Spatial Angle Wireframe Template in Evaluating Facial Asymmetry.Bioengineering (Basel, Switzerland) · 2025Article
- Automatic extraction of facial median sagittal plane for patients with asymmetry based on the EDMA alignment algorithm.Head & face medicine · 2024Article
- [Preliminary evaluation of chin symmetry with three dimentional soft tissue spatial angle wireframe template].Beijing da xue xue bao. Yi xue ban = Journal of Peking University. Health sciences · 2024Article
- Comparison Study of Extraction Accuracy of 3D Facial Anatomical Landmarks Based on Non-Rigid Registration of Face Template.Diagnostics (Basel, Switzerland) · 2023Article
- A mathematical algorithm of the facial symmetry plane: Application to mandibular deformity 3D facial data.Journal of anatomy · 2022Article
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Authors and funding
8 authors at 2 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The three-dimensional (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 'truth plane'. The 'position error' 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 'angle error' 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 ± 0.65° and 1.18 ± 0.62°, 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.
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