A mathematical algorithm of the facial symmetry plane: Application to mandibular deformity 3D facial data

Yujia Zhu; Xiangling Fu; Lei Zhang; Shengwen Zheng; Aonan Wen; Ning Xiao; Yong Wang; Yijiao Zhao

doi:10.1111/joa.13564

A mathematical algorithm of the facial symmetry plane: Application to mandibular deformity 3D facial data

J Anat. 2022 Mar;240(3):556-566. doi: 10.1111/joa.13564. Epub 2021 Nov 28.

Authors

Yujia Zhu^{1

2

3

4

5

6}, Xiangling Fu^{7

8}, Lei Zhang^{1

2

3

4

5

6}, Shengwen Zheng^{7

8}, Aonan Wen^{1

2

3

4

5

6}, Ning Xiao^{1

2

3

4

5

6}, Yong Wang^{1

2

3

4

5

6}, Yijiao Zhao^{1

2

3

4

5

6}

Affiliations

¹ Center of Digital Dentistry/Department of Prosthodontics, Peking University School and Hospital of Stomatology, Beijing, PR China.
² National Center of Stomatology, Beijing, PR China.
³ National Clinical Research Center for Oral Diseases, Beijing, PR China.
⁴ National Engineering Laboratory for Digital and Material Technology of Stomatology, Beijing, PR China.
⁵ Beijing Key Laboratory of Digital Stomatology, Beijing, PR China.
⁶ Research Center of Engineering and Technology for Computerized Dentistry Ministry of Health, Beijing, PR China.
⁷ School of Computer Science, Beijing University of Posts and Telecommunications (National Pilot Software Engineering School), Beijing, PR China.
⁸ Key Laboratory of Trustworthy Distributed Computing and Service, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, PR China.

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.

Keywords: aesthetics; facial asymmetry; oral diagnosis; orthodontics; orthognathic surgical procedures; three-dimensional imaging.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Cephalometry / methods
Face / anatomy & histology
Facial Asymmetry / diagnostic imaging
Humans
Imaging, Three-Dimensional* / methods
Mandible*