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

75A direct way to find a relationship between the MOS and each of the 37 traits is using Pearson’scorrelation coefficient. We remind the reader that for two vectors, X = x 1 ,x 2 ,...,x n andY = y 1 ,y 2 ,...,y n , the Pearson’s correlation coefficient is given byr X,Y = cov(X,Y)σ X σ Y= E[(X −µ X)(Y −µ Y )]σ X σ Y, (6.1)where σ X and σ Y are being the standard deviations for X and Y , respectively. The coefficientranges between −1 and 1, with the two extreme points being obtained when the variables aremaximally linearly related.Pearson’s correlation coefficients are calculated for all 37 vectors, each vector correspondingto a feature. Per feature, a 260-values X vector describes each feature for each one of the 260training images 1 . The 260–values vector Y describes each image related MOS rating. Table 6.1itemizes these coefficients in decreasing order of importance with respect to the absolute Pearson’scorrelation coefficient.6.4.2 Insight provided from empirical dataThe first notable result reveals the strong correlation between the best ranked traits and theMOS, which even exceeds a Pearson’s correlation coefficient of 0.5 for the trait ’ratio eyeheight/face-height’.Particularly in regard to an automatic MOS prediction image processing toolthese results are very encouraging. Further we observe that photo-quality features play a less significantrole than facial aesthetics, as expected, but they are not to be neglected, since they achieveanr 14,MOS = 0.168. Moreover we note that the high ranked traitsx 1 ,x 2 andx 4 , which representthe ratios (eye-height/face-height) and (head-width/head-height), and furthermore face shape, seeTable 6.1 are features corresponding strongly to person’s weight. This outcome brings to the forethe strong importance of low human weight for aesthetics. Furthermore it is worth noting thatTable 6.1 reveals the surprising fact among others, that non permanent traits place a pivotal rolein raising the MOS rating. Eye make-up, lipstick, glasses and hair-style are all among the top 11of the obtained ranking. These results hint the high modifiability of facial aesthetics perceptionby simple means like make-up or hair styling. The relevance of eye make-up had been previouslyobserved in [GKYG10]. Together with the different conclusions that one may draw from Table6.1, it also becomes apparent that different questions are raised, on the interconnectedness of thedifferent traits. This is addressed in Section 6.4.3. Finally we note that traits, such as x 1 , x 7 ,x 12 and x 13 directly comply with the well known babyfaceness hypothesis (see [bea11]), whichdescribes that childlike facial features in females increase attractiveness, such features include bigeyes, e.g. x 1 and a relative low location of facial elements, e.g. x 7 , x 12 and x 13 . One measureknown for increasing attractiveness, if equal to the golden ratio φ = 1.618, is x 16 .6.4.3 Interconnectedness of different traitsTo get a better understanding of the role of the different traits in raising theMOS, it is helpfulto study the inter-relationship between these traits. This is addressed in Table C.3 in the Appendix,which describes the correlation between selected traits. Due to lack of space we limit the correlationmatrix to just a group of the first six traits. Table C.3 can answer different questions such asfor example the validity of the conclusion in Table 6.1 on the importance of the make-up feature.In this case, the question arises whether it is truly the make-up that affects the MOS or whether1. For information on denotation of features and according X–values, please refer to the Appendix, Table C.2