Patterns of Facial Modularity by Hierarchical Facial Segmentation

Abstract

Objectives: To investigate patterns of facial modularity by hierarchical facial segmentation of global facial shape. Methods: 7,200 Han Chinese participants’ 3D facial images were captured using a stereophotogrammetric technique. The MeshMonk toolbox in MATLAB was used to ensure homology (i.e., point-to-point correspondence) for facial landmarks among all target faces. The method rapidly captured high-dimensional facial configurations while avoiding manual digitisation errors to realise “high-throughput phenotyping”. After rigid and non-rigid registration, each target face was represented by a spatially dense point cloud consisting of multiple 3D facial landmarks. Geometric morphometrics, a powerful analytical package, was used to extract and fully preserve shape information. The combined use of spatially dense landmark digitisation and geometric morphometrics enabled high-throughput facial phenotyping. An unsupervised machine learning algorithm partitioned each face into a series of stepwise focused facial modules; thus, even localised facial features (subdivided units) were analysed. The pairwise Covariance Ratio coefficient was computed for all landmarks, resulting in a squared similarity matrix that reflects the strength of association among facial landmarks. The modularity.test function of the geomorph package in R was used for CR coefficient estimation. Hierarchical spectral clustering was then performed to partition the face into global-to-local modules. This clustering was performed hierarchically such that each of the two clusters were further bifurcated. Facial modules covering stepwise focused facial regions were generated from global to local facial regions. Parallel analysis was applied to determine the optimal number of principal components used to represent each facial module. Results: High-dimensional facial shape data based on 7,160 facial landmarks that simulate the original facial configuration in high fidelity were generated. A total of 63 facial modules were yielded by hierarchical facial segmentation of global facial shape into five bifurcating levels. Conclusions: This hierarchical segmentation allowed high-throughput facial phenotyping at an unprecedented spatial resolution from global to local facial modules.