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

48 4. SEARCH PRUNING IN VIDEO SURVEILLANCE SYSTEMS Figure 4.4: Pruning process: categorization and elimination of categories.4.4 General settingFor this chapter, as mentioned above, we consider the setting where there is a search for asubject of interest v ′ , from within a larger authentication group of n subjects, v. The subject ofinterest v ′ is randomly placed inside v, and in turn v is randomly drawn from a larger population.Each member of v belongs to one of ρ categories C f ⊂ v, f = 1,··· ,ρ, with probability equalto|C f |p f := E v , f = 1,··· ,ρ, (4.4)nwhere E is used to denote the statistical expectation. Such category can be for example (labeledas) ’blue eyed, with moustache and with glasses’. The soft biometric system goes through theelements v ∈ v, and provides an estimate Ĉ(v) ∈ [1,ρ] of the category that v belongs in. For C′denoting the actual category of v ′ , where this category is considered to be known to the system,then each element v is pruned out if and only ifĈ(v) ≠ C′ . Specifically the SBS produces a setS = {v ∈ v : Ĉ(v) = C ′ } ⊂ vof subjects that were not pruned out. The pruning gain comes from the fact that S is generallysmaller than v.It is the case that pruning which results in generally smaller S, is associated to a higher gain,but also a higher risk of erroneously pruning out the target subject v ′ , thus reducing the reliabilityof the SBS. Both reliability and pruning gain are naturally affected by different parameters suchas– the category distribution of the authentication group v,– the distinctiveness of the category to which v ′ belongs– the system design: a conservatively tuned system will prune only with low risk to prune outv ′ , allowing for a high false acceptance rate FAR, on the other hand an aggressive systemwill prune stronger with the cost of a higher false rejection rate FRR.Furthermore, the gain is clearly a function ofv. Consequently any meaningful analysis of an SBSwill have to be statistical in nature. We here consider the average behavior of such systems. Insuch a case we will see that two aspects prove to be crucial in defining the average case behaviorof the system. The first aspect is the population statistics and the second is the error behavior ofthe different categorization algorithms. Specifically we here consider the vectorp := [p 1 ,p 2 ,··· ,p ρ ] T (4.5)which defines the entire population statistics. In terms of error behavior, we defineɛ ij := P(Ĉ(v) = C j : v ∈ C i ) (4.6)