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

5710.950.9pruning Gain r(vt)0.850.80.750.70.650 5 10 15 20 25 30Realization tFigure 4.10: SBS ‘emg’, n=20, target subjectv ′ belongs to categoryC ′ =“Blue eyes - no moustache- no glasses".error given byand an average gain ofP err = p T er := E v,w r(v) = 1−p T Ep. (4.29)A relevant question is whether it is better, in terms of increasing the average gain, to invest insoft biometric traits like tattoos, scars and birth marks, which are rare, but distinctive, or if it is ofmore value to invest in facial measures and facial colors, in which subjects are distributed moreuniformly. The above proposition addresses this question and can show that investing towards auniform category distribution for a given population is most valuable in terms of gain.We illustrate the average gain and pruning error for the proposed SBSs in Figure 4.11 andprovide the exact values in Table 2.At this point we can establish also the measure of goodput, which was introduced in 4.5.1 as ameasure that jointly considers both the gain and the reliability capabilities of an SBS.Average goodput of search pruning The measure of goodput, combines as introduced in 4.5.1the pruning gain with reliability. For the sake of simplicity the measure, denoted here as U, takesthe form of a weighted product between reliability and gainU := (1−P err ) γ 1r γ 2(4.30)for some chosen positive γ 1 ,γ 2 that respectively describe the importance paid to reliability andto pruning gain. We note the change of the expression from section 4.5.1, which forms thoughare both equivalent. We proceed to evaluate and rank the given SBSs in terms of the introducedcharacteristics gain, error and goodput and set hereby the tuning variables γ 1 = γ 2 = 1.Table 4.7.1 provides the results on the proposed nine SBSs. We observe that the highestgoodput is attributed to system ‘4e’ endowed with 4 eye color categories. The enhanced systems‘2emg’ and ‘4emg’ introduce a gain increase, but at the cost of an increased error probability. Onthe other hand the systems ‘2e’, ‘m’, ‘g’, and ‘2eg’ introduce lower error probabilities but at acost of low average pruning gain. The intertwined relationship between error, gain and goodputis illustrated in Figure 4.11. Given the measure of goodput we can compare SBSs, by prioritizing