FACIAL SOFT BIOMETRICS - Library of Ph.D. Theses | EURASIP

76 6. SOFT BIOMETRICS FOR QUANTIFYING AND PREDICTING FACIAL AESTHETICSalready attractive subjects use make-up more heavily. Table C.3 suggests a low correlation betweenthe facial proportions (representing beauty) and eye make-up, which validates the strongrole of makeup in raising the MOS.6.5 Model for facial aestheticsWe choose a linear metric due to its simplicity and the linear character of the traits with increasingMOS. We perform multiple regression with the multivariate data and obtain a MOSestimation metric with the following form:∑37̂MOS = γ i x i . (6.2)The resulting weights γ i corresponding to each trait are denoted in Table 6.1.We here note that the weights of the model are not normalized and do not give informationabout the importance of each characteristic. With other words, we did not normalize for the sakeof reproducibility - ̂MOS can be computed with features labeled as in Table C.1 and Table C.2 inAppendix C and related weights from Table 6.1. The importance of the characteristics is conveyedby the Pearson’s correlation coefficients r Xi ,MOS.6.5.1 Validation of the obtained metricTo validate our model we compute the following three parameters.– Pearson’s correlation coefficient. As described above, and it is computed to bei=1r̂MOS,MOS= 0.7690. (6.3)– Spearman’s rank correlation coefficient, which is a measure of how well the relation betweentwo variables can be described by a monotonic function. The coefficient rangesbetween -1 and 1, with the two extreme points being obtained when the variables are purelymonotonic functions of each other. This coefficient takes the formr S = 1− 6∑ i d in(n 2 −1) , (6.4)whered i = rank(x i )−rank(y i ) is the difference between the ranks of thei th observationof the two variables. The variable n denotes the number of observations. The coefficient,which is often used due to its robustness to outliers, was calculated here to ber ŜMOS,MOS= 0.7645. (6.5)– Mean standard error of the difference between the estimated objective ̂MOS and the actualsubjective MOS.MSE = 0.7398 (6.6)These results clearly outperform the outcomes from Eigenfaces of = 0.18, as well asr̂MOS,MOS)neural = 0.458 (see [GKYG10]), but the comparison is not very adequate asnetworksr̂MOS,MOSwe would compare manual extraction with automatic extraction of facial aesthetics. Neverthelessthe potential of our approach is evident and we proceed with a robust validation of the facialaesthetics metric. For this purpose we annotated the 37 traits beyond the training set, in an extratesting set of 65 images. Once more we excluded outliers (3 images) and we computed the metricverification measures for the estimated ̂MOS and the according actual MOS