A PCA-Based method for determining craniofacial relationship and sexual dimorphism of facial shapes

Previous studies have used principal component analysis (PCA) to investigate the craniofacial relationship, as well as sex determination using facial factors. However, few studies have investigated the extent to which the choice of principal components (PCs) affects the analysis of craniofacial relationship and sexual dimorphism. In this paper, we propose a PCA-based method for visual and quantitative analysis, using 140 samples of 3D heads (70 male and 70 female), produced from computed tomography (CT) images. There are two parts to the method. First, skull and facial landmarks are manually marked to guide the model's registration so that dense corresponding vertices occupy the same relative position in every sample. Statistical shape spaces of the skull and face in dense corresponding vertices are constructed using PCA. Variations in these vertices, captured in every principal component (PC), are visualized to observe shape variability. The correlations of skull- and face-based PC scores are analysed, and linear regression is used to fit the craniofacial relationship. We compute the PC coefficients of a face based on this craniofacial relationship and the PC scores of a skull, and apply the coefficients to estimate a 3D face for the skull. To evaluate the accuracy of the computed craniofacial relationship, the mean and standard deviation of every vertex between the two models are computed, where these models are reconstructed using real PC scores and coefficients. Second, each PC in facial space is analysed for sex determination, for which support vector machines (SVMs) are used. We examined the correlation between PCs and sex, and explored the extent to which the choice of PCs affects the expression of sexual dimorphism. Our results suggest that skull- and face-based PCs can be used to describe the craniofacial relationship and that the accuracy of the method can be improved by using an increased number of face-based PCs. The results show that the accuracy of the sex classification is related to the choice of PCs. The highest sex classification rate is 91.43% using our method.