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

29Table 3.1: SBSs with symmetric traits instancesµ\λ 2 3 4 5 62 4 8 16 32 643 9 27 81 243 7294 16 64 256 1024 40965 25 125 625 3125 156256 36 216 1296 7776 46656Table 3.2: Augmented set of facial soft biometric traits and corresponding number of instancesSkin Hair Eye Glasses Beard Moustache Age GenderColor Color Color Presence Presence Presence3 8 6 2 2 2 3 2Make up Facial Facial feature Facial Facial feature Facial moles HairShapes Shapes measurements measurements and marks style4 3 3 3 6 6 3This approach in turn, brings to the fore the issue that increasing ρ, may indeed result in anincreased E[ρ e ], but might affect the correlation between the different categories. This wouldsubsequently result in a reduced spread of Φ, which would imply a reduced distinctiveness inidentification. In regards to this, we give some intuition on the distinctiveness of some non-emptycategories of the proposed system, by computing the correlation between these categories usingPearson’s product-moment coefficientr X,Y = cov(X,Y)σ X σ Y= E[(X −µ X)(Y −µ Y )]σ X σ Y(3.6)The resulting correlation parameters shown belowr EyeColor,HairColor = −0.1964 (3.7)r HairColor,SkinColor = −0.1375 (3.8)r EyeColor,SkinColor = 0.370 (3.9)r Moustache,Beard = 0.6359 (3.10)revealed as expected the highest correlation to be that between moustache and beard.Further intuition on related correlations is given in Figure 3.3, which shows the joint pdf withrespect to the eye, skin and hair color.Figure 3.3: Color based soft biometric traits (eye-hair, eye-skin and hair-skin color) distributionsfor FERET database.