How does the use of multiple fingers affect a verification?
There are two extreme cases: • All N (N<11) fingers must be recognized • For N>1, at least 1 Finger must be recognized In Case 1, the false acceptance rate FAR improves (provided that the fingers n (0 < n < N+1) are statistically independent) according to: FAR = FAR1FAR2FAR3···FARN where FARn is the FAR of finger n => FAR = FAR1N if all FARn equal FAR1 while the false rejection rate gets worse: FRR = 1 – (1 – FRR1)(1 – FRR2)(1 – FRR3)···(1 – FRRN) => FRR = 1 – (1 – FRR1)N if all FRRn equal FRR1 => FRR ~ N·FRR1 if additionally N·FRR1 << 1 In Case 2 it is exactly the opposite: FAR = 1 - (1 - FAR1)(1 - FAR2)(1 - FAR3)···(1 - FARN) => FAR = 1 – (1 – FAR1)N if all FARn equal FAR1, n = 2,…,N => FAR ~ N·FAR1 if additionally N·FAR1 << 1 and for the FRR: FRR = FRR1FRR2FRR3···FRRN => FRR = FRR1N if all FRRn equal FRR1, n = 2,…,N Note that the assumption of statistic independence appears justifiable based on the hypothesis of uniqueness. Imperfections such as a dirty finger generally, however
