A Quantitative Approach to Predict Ageing in Midsagittal Facial Profile

The aim of the present study was to introduce a quantitative method using Fourier analysis to predict ageing in midsagittal facial profile. Midsagittal facial profiles were extracted as lists of X-Y coordinates from 125 pairs of 3D facial scans captured at an average of 10.5 years apart for adult Japanese males aged 23-52 years. Coordinate files were categorized into three 10-year-long age groups and underwent Fourier analysis. In a test set of 10 individuals randomly selected from each age group, the predicted Fourier coefficients were calculated for each of the tested individuals using a leave-one-out linear regression analysis at each harmonic level. This was accomplished by regressing the corresponding post-ageing coefficients onto pre ageing coefficients. The accuracy of predicted ageing coefficients were tested as the sum of squared errors between predicted and the actual post ageing coefficients (SSE pre ageing vs. post ageing ) in contrast to the errors between the pre and post ageing coefficients (SSE Post ageing vs. Predicted ageing ) using a paired t-test (α=0.05) across all tested individuals. Paired t-test showed that SSE pre ageing vs. post ageing were significantly larger than SSE Post ageing vs. Predicted ageing (p = 0.034) indicating that the coefficients of the predicted ageing are significantly closer to their corresponding actual post ageing coefficients than to the pre ageing coefficients. By using Fourier analysis, a quantitative prediction model for ageing in the midsagittal facial profile was introduced with some statistically supported accuracy. Testing the model further on other parasagittal and transverse facial contours and on younger and older age groups may open the gate towards possible applications in various disciplines of forensic science and clinical medicine. The aim of the present study was to introduce a quantitative method using Fourier analysis to predict ageing in midsagittal facial profile. Midsagittal facial profiles were extracted as lists of X-Y coordinates from 125 pairs of 3D facial scans captured at an average of 10.5 years apart for adult Japanese males aged 23-52 years. Coordinate files were categorized into three 10-year-long age groups and underwent Fourier analysis. In a test set of 10 individuals randomly selected from each age group, the predicted Fourier coefficients were calculated for each of the tested individuals using a leave-one-out linear regression analysis at each harmonic level. This was accomplished by regressing the corresponding post-ageing coefficients onto pre ageing coefficients. The accuracy of predicted ageing coefficients were tested as the sum of squared errors between predicted and the actual post ageing coefficients (SSE pre ageing vs. post ageing ) in contrast to the errors between the pre and post ageing coefficients (SSE Post ageing vs. Predicted ageing ) using a paired t-test (α=0.05) across all tested individuals. Paired t-test showed that SSE pre ageing vs. post ageing were significantly larger than SSE Post ageing vs. Predicted ageing (p = 0.034) indicating that the coefficients of the predicted ageing are significantly closer to their corresponding actual post ageing coefficients than to the pre ageing coefficients. By using Fourier analysis, a quantitative prediction model for ageing in the midsagittal facial profile was introduced with some statistically supported accuracy. Testing the model further on other parasagittal and transverse facial contours and on younger and older age groups may open the gate towards possible applications in various disciplines of forensic science and clinical medicine.