Fig 1.
The landmarks and semilandmarks used for the shape analysis (black circles) and the image warping (grey disks) are shown on the average face texture deformed to the average face shape.
Table 1.
Descriptive statistics for body mass index (BMI) and waist-to-hip ratio (WHR): mean, standard deviation, range (min-max), and the three quartiles.
Fig 2.
Scree plots for (A) face shape and (B) face texture, showing the fractions of variance accounted for by the corresponding principal components.
Fig 3.
Principal component (PC) scores of (A) face shape (landmark shape coordinates) and (B) face texture (RGB values of the standardized images). Each disk represents one individual, where the diameter of the disk is proportional to the individual’s BMI. In (A) the distances between points approximate the shape differences (Procrustes distance) between the corresponding individuals’ faces, whereas in (B) the distances approximate differences in face texture (squared differences in RGB values, summed over all pixels). The solid red lines are the directions in these two-dimensional PC spaces with maximal increase in body mass index (the coefficient vector of the regression of shape on BMI, projected onto PC 1 and 2); the dashed red lines are the directions of maximal increase in waist-to-hip ratio (WHR).
Fig 4.
Visualization of the first two principal components (PCs) of face shape (upper panel) and face texture (lower panel).
The individual PC scores for these shape and texture features are plotted in Fig 3. The reconstructed faces correspond to a deviation of 0.5 units (Procrustes distance) and 20,000 units from the mean shape and mean texture, respectively, which approximately corresponds to the occurring range of variation along PC1 and to a twofold extrapolation of this range along PC 2.
Fig 5.
Regressions of shape (upper panel), texture (middle panel), as well as both together (lower panel) on BMI.
The reconstructed faces represent the average shapes and textures predicted for BMI 15, 23, and 31, respectively, based on these regressions. These are ±2 standard deviations around the average BMI of 23 and approximately represent the range of variation observed in our sample. The left-most and right-most faces in the figure are twofold extrapolations of this range; they correspond to deviations of ±4 standard deviations from the mean and to (hypothetical) BMIs of 7 and 39.
Fig 6.
Regression of facial texture on BMI, visualized for each color channel (R, G, B) separately.
In contrast to Fig 5, here the RGB values of each pixel were corrected to keep brightness constant (i.e., they were mean-centered separately for each pixel) to focus on the association of hue with BMI.
Fig 7.
Regressions of shape (upper panel), texture (middle panel), as well as both together (lower panel) on waist-to-hip ratio (WHR).
The reconstructed faces represent the average shapes and textures predicted for WHR 0.63, 0.72, and 0.81, respectively, based on these regressions. These are ±2 standard deviations around the average WHR of 0.72 and approximately represent the limits of variation observed in our sample. The left-most and right-most faces in the figure are twofold extrapolations of this range; the correspond to deviations of ±4 standard deviations from the mean and to (hypothetical) WHRs of 0.54 and 0.90.