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

46 4. SEARCH PRUNING IN VIDEO SURVEILLANCE SYSTEMS ̷ ̷ 10987654ρ = 3, p 1= 0.1ρ = 8, p 1= 0.130 0.05 0.1 0.15 0.2 0.25 0.3 0.35Figure 4.2: Pruning gain, as a function of the confusability probability ɛ, for the uniform errorsetting, and for p 1 = 0.1. Plotted for ρ = 3 and ρ = 8.whether searching for a rare looking subject renders the search performance more sensitive toincreases in confusability, than searching for common looking subjects. We then present nine differentsoft biometric systems, and describe how the employed categorization algorithms (eye colordetector, glasses and moustache detector) are applied on a characteristic database of 646 people.In Section 4.6.1 we provide simulations that reveal the variability and range of the pruning benefitsoffered by different SBSs. In Section 4.7 we provide concise closed form expressions on themeasures of pruning gain and goodput, provide simulations, as well as derive and simulate aspectsrelating to the complexity costs of different soft biometric systems of interest.Before proving the aforementioned results we hasten to give some insight, as to what is tocome. In the setting of large n, Section 4.5.1 easily tells us that the average pruning gain takesthe form of the inverse of ∑ ρf=1 p fɛ f , which is illustrated in an example in Figure 4.2 for different(uniform) confusability probabilities, for the case where the search is for an individual thatbelongs to a category that occurs once every ten people, and for the case of two different systemsthat can respectively distinguish 3 or 8 categories. The atypical analysis in Section 4.5 is moreinvolved and is better illustrated with an example, which asks what is the probability that a systemthat can identify ρ = 3 categories, that searches for a subject of the first category, that has 80percent reliability, that introduces confusability parameters ɛ 2 = 0.2,ɛ 3 = 0.3 and operates over apopulation with statistics p 1 = 0.4,p 2 = 0.25,p 3 = 0.35, will prune the search to only a fractionof τ = |S|/n. We note that here τ is the inverse of the pruning gain. We plot in Figure 4.3 theasymptotic rate of decay for this probability,logJ(τ) := − lim P(|S| > τn) (4.1)N→∞ n/ρfor different values of τ. From the J(τ) in Figure 4.3 we can draw different conclusions, such as:– Focusing on τ = 0.475 where J(0.475) = 0, we see that the size of the (after pruning) setS is typically (most commonly - with probability that does not vanish withn)47.5% of theoriginal size n. In the absence of errors, this would have been equal to p 1 = 40%, but theerrors cause a reduction of the average gain by about 15%.– Focusing onτ = 0.72, we note that the probability that pruning removes less than1−0.72 =28% of the original set is approximately given by e −n , whereas focusing on τ = 0.62, we