A fingerprint scanner that embeds a fake finger detection mechanism has to decide, for each transaction, if the current sample comes from a real finger or from a fake one. This decision will be unavoidably affected by errors, that should be as low as possible: in particular, a scanner could reject real fingers and/or accept fake fingers, independently of the user’s identity.
Let us assume the below:
\(FRR_{fd}\) - the proportion of real-finger transactions where the system incorrectly considered the input to come from a fake sample
\(FRR_{iv}\) - the proportion of fake-finger transactions where the system incorrectly considered the input to come from a real finger
\(FAR_{fd}\) & \(FAR_{iv}\) - the identity verification error rates
The fake-detection mechanism, the overall FRR error can be estimated as
\(FRR\ =FRR_{fd}+\left(1-FRR_{fd}\right)\cdot FRR_{iv}\) (for an authorized user trying to be authenticated normally using the real enrolled finger)
the overall FAR error can be estimated as:
\(FAR^{Real-NonEnrolled}=\left(1-FRR_{fd}\right)\cdot FAR_{iv}\) (for an attacker trying to be authenticated using a real finger, different from the enrolled one)
And the two below will be the ones we will be interested in: