Score-level fusion based on the direct estimation of the Bayes error gradient distribution

This paper describes a method of score-level fusion to optimize a Receiver Operating Characteristic (ROC) curve for multimodal biometrics. When the Probability Density Functions (PDFs) of the multimodal scores for each client and imposter are obtained from the training samples, it is well known that the isolines of a function of probabilistic densities, such as the likelihood ratio, posterior, or Bayes error gradient, give the optimal ROC curve. The success of the probability density-based methods depends on the PDF estimation for each client and imposter, which still remains a challenging problem. Therefore, we introduce a framework of direct estimation of the Bayes error gradient that bypasses the troublesome PDF estimation for each client and imposter. The lattice-type control points are allocated in a multiple score space, and the Bayes error gradients on the control points are then estimated in a comprehensive manner in the energy minimization framework including not only the data fitness of the training samples but also the boundary conditions and monotonic increase constraints to suppress the over-training. The experimental results for both simulation and real public data show the effectiveness of the proposed method.