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

31corresponding to p(n,ρ). Towards generalizing, we deviate from the uniformity assumption, torather consider a more realistic setting where the category distribution originates from an onlinesurvey (see [hai10]), of 5142 subjects from Central Germany. For computational simplicity wechoose to consider a simpler, reduced version of our proposed system, where the traits are limitedto hair color and eye color. In this setting, the hair color trait has 7 trait-instances, and theeye color trait has 5 trait instances, resulting in a total of ρ = 35 categories, with probabilitiesP(φ i ),i = 1,...,35.In this case the probability that all n subjects are in different categories is the sum of theproducts of all non-colliding events [JDP92]:p non_collision (n) = ∑i≠j≠···≠zP(φ i )P(φ j )...P(φ z ) (3.17)where the summation indexing corresponds to the non-empty categories with respect to the authenticationgroup.3.4.3 Simulation evaluation of the system in the interference limited settingIn the following we provide a simulation of the probability of identification error, in the settingof interest, under the assumption that the errors are due to interference, i.e., under the assumptionsthat errors only happen if and only if the chosen subject shares the same category with anotherperson from the randomly chosen authentication group. This corresponds to the setting wherethe soft-biometric approach cannot provide conclusive identification. In the simulation, the largerpopulation consisted of 646 people from the FERET database, and the simulation was run fordifferent sizes n of the authentication group. The probability of identification error is described inthe following figure.Probability of Collision10.90.80.70.60.50.40.30.20.10p(N) all traitsp(N) no glassesp(N) no skin colorp(N) no hair colorp(N) no eye colorq(N) all traitsq(N) no glassesq(N) no skin colorq(N) no hair colorq(N) no eye color2 4 6 8 10 12 14Subjects NFigure 3.4: Collision probability in an n sized authentication group.As a measure of the importance of each trait, Figure 3.4 describes the collision probabilitywhen different traits are removed. The presence of moustache and beard seem to have the leastinfluence on the detection results, whereas hair and eye color have the highest impact on distinctiveness.