A Metric of Information Gained Through Biometric Systems

We propose a metric of information gained through biometric matching systems. Firstly, we discuss how the information about the identity of a person is derived from biometric samples through a biometric system, and define the "biometric system entropy" or BSE. Then we prove that the BSE can be approximated asymptotically by the Kullback-Leibler divergence $D(f_G(x) | | f_I(x))$ where $f_G(x), f_I(x)$ are PDFs of matching scores between samples from an individuals and among population. We also discuss how to evaluate $D(f_G | | f_I)$ of a biometric system and show a numerical example of face and fingerprint matching systems.