A series of 26 anatomical surface landmarks were then collected from each participant’s 3D facial scan, and the corresponding x,y,z coordinates saved. From these landmark coordinates, a set of 29 simple linear distances were calculated using simple Euclidean geometry. These 29 distances are equivalent to standard facial anthropometric measurements (Farkas 1994; Kolar and Salter, 1997) and are shown above in Table 1 and Table 2.
In addition to simple linear distance measures, seven commonly used anthropometric indices were calculated from these distances (shown below in Table 3). These proportions provide a rudimentary way of capturing shape information on the face (Farkas and Munro, 1987).
Table 3: List of craniofacial indices used in the present study
Higher values indicate a relatively shorter and/or wider nose
Simple univariate statistics were run to compare males and females across the entire set of 41 craniofacial measurements and indices (5 distances from direct anthropometry; 29 distances from 3D photogrammetry; and 7 indices). Tests were run two different ways: (1) independent samples t-tests were performed and (2) analysis of covariance (ANCOVA) was carried out on the same variables, with the subject’s height included as a covariate. The second set of tests was performed to assess whether any craniofacial measures were significantly different even after adjusting for the effects of overall body size, since it is well known that males are larger on average. Comparing height in our dataset revealed this same pattern, with males showing a mean height increase of 15.4 cm over females (p < 0.001). To adjust for multiple comparisons, a Bonferonni correction was applied to the p-value and the threshold for statistical significance was set to 0.001 (.05/41).
The descriptive statistics of the five direct anthropometric measurements and 29 3D surface-derived measurements are presented in Table 4. Of note, the positive mean difference values were all signed positive, indicating that all 34 dimensions were larger in our male sample. The inferential statistics are presented in Table 5. The t-tests showed that mean difference between males and females was significant for 32 of the 34 measurements at the p < 0.001 level. Only two of the 34 measurements were found to be non-significant, and these were upper vermilion height (p = 0.109) and lower vermilion height (p = 0.046), both relating to the vermillion segment of the lips. When the means were adjusted for the covariate ‘height’, the analysis of covariance (ANCOVA) still revealed significant differences for 27 of the 34 measurements at the p < 0.001 level. Five of the 34 measurements were no longer found to be statistically significant, and these were minimum frontal width (p = 0.011), palpebral fissure length (right) (p = 0.203), palpebral fissure length (left) (p = 0.277), nasal protrusion (p = 0.01), and nasal height (p = 0.014). Both upper vermilion height (p = 0.940) and lower vermilion height (p = 0.202) remained non-significant.
Table 6 summarizes the seven calculated craniofacial indices as well as the results of the accompanying t-tests. Males were found to have larger facial, intercanthal, and nasal indices while females were found to have larger cephalic, upper facial, upper-middle facial depth, and middle-lower facial depth indices. Of the 7 indices calculated, four were found to be non-significant, and these were the cephalic (p = 0.103), facial (p = 0.094), upper facial (p = 0.082), and intercanthal (p = 0.444) indices. Conversely, the remaining three indices (upper-middle facial depth, middle-lower facial depth, and nasal) were found to be significant at the p < 0.001 level.
Table 4: Descriptive statistics on all 34 craniofacial measurements (mm)