A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm

Zhu, Yujia; Zheng, Shengwen; Yang, Gongping; Fu, Xiangling; Wen, A N; Wang, Yong; Zhao, Yijiao

doi:10.1186/s12903-020-01311-3

Cited by 15 publications

(16 citation statements)

References 28 publications

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“…This method can be employed to localize and visualize areas of increased asymmetry. The method usually involves 3D surface data acquisition, mirroring of the surface and matching the surfaces via a best-fit algorithm [45][46][47]. For the latter purpose, the Iterative Closest Point algorithm (ICP) can be used [48].…”

Section: Asymmetry Quantificationmentioning

confidence: 99%

Symmetry and Aesthetics in Dentistry

Runte

Dirksen

2021

Symmetry

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Animal bodies in general and faces in particular show mirror symmetry with respect to the median-sagittal plane, with exceptions rarely occurring. Bilateral symmetry to the median sagittal plane of the body also evolved very early. From an evolutionary point of view, it should therefore have fundamental advantages, e.g., more effective locomotion and chewing abilities. On the other hand, the recognition of bilaterally symmetric patterns is an important module in our visual perception. In particular, the recognition of faces with different spatial orientations and their identification is strongly related to the recognition of bilateral symmetry. Maxillofacial surgery and Dentistry affect effective masticatory function and perceived symmetry of the lower third of the face. Both disciplines have the ability to eliminate or mitigate asymmetries with respect to form and function. In our review, we will demonstrate symmetric structures from single teeth to the whole face. We will further describe different approaches to quantify cranial, facial and dental asymmetries by using either landmarks or 3D surface models. Severe facial asymmetries are usually caused by malformations such as hemifacial hyperplasia, injury or other diseases such as Noma or head and neck cancer. This could be an important sociobiological reason for a correlation between asymmetry and perceived disfigurement. The aim of our review is to show how facial symmetry and attractiveness are related and in what way dental and facial structures and the symmetry of their shape and color influence aesthetic perception. We will further demonstrate how modern technology can be used to improve symmetry in facial prostheses and maxillofacial surgery.

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Section: Asymmetry Quantificationmentioning

confidence: 99%

Symmetry and Aesthetics in Dentistry

Runte

Dirksen

2021

Symmetry

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“…In oral clinical practice, physicians tend to focus more on the landmarks with good facial symmetry (i.e., landmarks around the eyes, nose and mouth). Therefore, the power function y = x α ( α = −1) was used in our previous study to demonstrate the trend in which the weight decreases with the increase of asymmetry (Zhu et al, 2020). After the initialisation of the original method and the mirror model overlaps, the landmarks with poor symmetry (in which the distance of the original mirror paired landmarks is larger) are assigned smaller weights.…”

Section: Discussionmentioning

confidence: 99%

“…In this study, the SP and OP functions were used to achieve the effect of a landmark pair with good symmetry that would be relatively close together after initial registration and, thus, would be given more weight. The weights of all the anatomical landmarks were distributed in a reasonable domain which was more appropriate than the previous WPA algorithm (Zhu et al, 2020). The weighted landmarks of LMK_Org and LMK_Mir were superimposed three‐dimensionally based on the least‐squares method; thus, optimal overlapping was obtained for the 32 pairs of landmarks, and the SPWPA and OPWPA transformation matrices of Model_Mir were obtained.…”

Section: Methodsmentioning

confidence: 99%

“…However, for patients with noticeable facial asymmetry, this method is not ideal because the algorithm assigns equal weight to individualised facial features without discrimination, which deviates from the rationale followed in clinical diagnosis. Zhu et al (2020) proposed the weighted Procrustes analysis (WPA) algorithm which provides a more adaptable SRP than the standard PA algorithm when applied to mandibular deviation patients.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

Zhang

et al. 2021

Journal of Anatomy

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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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“…Including laser scanning system, cast-analyzing software [13,14], and beta function [15,25] to provide curve fitting, various varieties of mathematical methods were applied to fit for basal arch forms. For average enclosed contour analysis, the Generalized Procrustes Analysis (GPA) suited more for shape registration and quantitive illustration [26], which was wide as a morphometric analysis approach for medical morphometric data [27,28]. The Principal Component Analysis (PCA), which was widely applied in the evaluation of shape variation [29][30][31], used the dimensionality reduction technique to replace the original multiple variables and obtained the contribution rate of each principal component by calculating the score of the comprehensive principal component functions to evaluate the multivariate.…”

Section: Introductionmentioning

confidence: 99%

Match of the Bimaxillary Basal Bone Arches and Its Variations among Individuals

et al. 2021

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Introduction. This study is aimed at illustrating the bimaxillary basal bone contours, to clarify the match of the basal bone arches of the upper and lower, especially the posterior segments, including the second molar and retromolar region. Methods. Based on 100 cone-beam computed tomography (CBCT) images (50 males and 50 females), we obtained 100 pairs of basal bone arches, which were the horizontal inner cortex contours passing the furcation of the first molar paralleled to the lower occlusal plane. The Generalized Procrustes Analysis (GPA) was applied to depict average contours and calculate the ratio and difference width of both upper and lower dental arches in different positions. Variations of the basal bone morphology among individuals were revealed using Principal Component Analysis (PCA). Results. The width discrepancy occurred at 7-7 segment (male: upper 65.62 mm and lower 68.81 mm and female: upper 62.98 mm and lower 68.38 mm) and the retromolar region (male: upper 64.67 mm and lower 71.96 mm and female: upper 62.34 mm and lower 71.44 mm). The ratio ( p = 0.006 ) and difference value ( p = 0.009 ) of 7-7 segment and the ratio of retromolar region ( p = 0.044 ) differed in genders. Setting 2 mm overjet, the upper basal bone arch was wider than the lower by approximate 2 mm on both sides, except the second molar and retromolar region. According to PCA, the variation of basal bone arches appeared mainly at terminal segments. Conclusions. For both male and female, the bimaxillary basal bone matched except terminal segments. Mismatch of female bimaxillary posterior basal bone was more pronounced than male. The basal bone arches of male were wider and longer than that of female.

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A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm

Cited by 15 publications

References 28 publications

Symmetry and Aesthetics in Dentistry

Symmetry and Aesthetics in Dentistry

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

Match of the Bimaxillary Basal Bone Arches and Its Variations among Individuals

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