Toward Optimal Fusion Algorithms With Security Against Wolves and Lambs in Biometrics

It is known that different users have different degrees of accuracy in biometric authentication, and claimants and enrollees who cause false accepts against many others are referred to as wolves and lambs, respectively. The aim of this paper is to develop a fusion algorithm, which has security against both of the animals while minimizing the number of query samples a genuine claimant has to input. To achieve our aim, we first introduce a taxonomy of wolves and lambs, and propose a minimum log-likelihood ratio-based sequential fusion scheme (MLR scheme). We prove that this scheme keeps wolf attack probability and lamb accept probability, the maximum of the claimant-specific false accept probability (FAP), and the enrollee-specific FAP, less than a desired value if log-likelihood ratios are perfectly estimated, except in the case of adaptive spoofing wolves. We also prove that this scheme is optimal with regard to false reject probability (FRP), and asymptotically optimal with respect to the average number of inputs (ANIs) under some conditions. We further propose an input order decision scheme based on the Kullback-Leibler (KL) divergence, which maximizes the expectation of a genuine log-likelihood ratio, to further reduce ANI of the MLR scheme in the case where the KL divergence differs from one modality to another. The results of the experimental evaluation using a virtual multimodal (one face and eight fingerprints) data set showed the effectiveness of our schemes.