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

11Notations used in this workE : statistical expectationα 0,f (v)} ρ f=1 : instantaneous normalized distribution (histogram) of{|C f|} ρ f=1for a specific vɛ f : categorization or confusion error probabilitieŝφ : algorithmically estimated category φλ : soft biometric trait instancesG(v) : pruning gain G(v) := n|S|S : subset of n of subjects that were not pruned outU : goodputV(τ) : set of valid α for a given τµ : soft biometric traitφ : λ–tuple of different trait–instances, one possible category: ’blue eyed, with moustache andwith glasses’Φ : Φ = {φ i } ρ i=1set of all ρ categoriesρ : total number of categoriesτ : inverse of pruning gain, τ = |S|/nĈ(v) ∈ [1,ρ] : Category that v belongs inACT : absolute category ratingC ′ : actual category of v ′C f ⊂ v, f = 1,··· ,ρF : number of effective or non-empty categories spanned byvMOS : mean opinion scoreN : computational complexityn : size of authentication groupP err : error probability P(err|v) : probability of erroneously identifying a subjectP φ : probability of incorrectly identifying a subject from S φp f : p f : population statisticsr : relative throughput of a SBS,r := lim ρ→∞nρS : subset of v that remains after pruningS φ ⊂ v : set of subjects inv that belong in a specific category φS id : set of subjects in v that can potentially be identified by a SBS ’endowed’ with Φ, S i d :=∪ F φ=1 S φv : elements in vv ′ : subject of interest in the context of search pruningv : authentication group containing n subjectsv(i), i = 1,...,n : i-th candidate belonging to the specific group vSB : soft biometricsSBS : soft biometric system