Decision making in the LDA space: generalised gradient direction metric

We consider the problem of face authentication in the linear discriminant analysis (LDA) space and investigate the effect of different scoring functions on the performance of the authentication system. First the theory of optimal metric for measuring the similarity between a pair of face images presented in J. Kittler et al. (2000) is extended to cope with general class specific covariance structures. The resulting gradient metric is experimentally compared with the commonly used normalised correlation and the original gradient metric. The merit of global and client specific thresholding is also investigated. The study is performed on the BANCA database [E. Bailly-Bailliere et al., 2003] using internationally agreed experimental protocols. The results suggest that the novel metric is superior in scenarios where the quality of input face data is comparable to the quality of data used for determining the LDA space. In other cases, the weaker model deploying the isotropic covariance matrix in working out the gradient direction is preferable.