Continuous Distribution Approximation and Thresholds Optimization in Serial Multi-Modal Biometric Systems

  • Milan Stanojević,
  • Ivan Milenković
  • Dušan Starčević
  • Bogdana Stanojević


Multi-modal biometric verification systems use information from several biometric modalities to verify an identity of a person. The false acceptance rate (FAR)and false rejection rate (FRR) are metrics generally used to measure the performance of such systems.In this paper, we first approximate the score distributions of both genuine users and impostors by continuous distributions. Then we incorporate the exact expressions of the distributions in the formulas for the expected values of both FAR and FRR for each matcher. In order to determine the upper and lower acceptance thresholds in the sequential multi-modal biometric matching, we further minimize the expected values of FAR and FRR for the entire processing chain. We propose a non-linear bi-objective programming problem whose objective functions are the two error probabilities. We analyze the efficient set of the bi-objective problem, and derive an efficient solution as a best compromise between the error probabilities. Replacing the least squares approximation of the score distributions by a continuous distributionapproximation, this approach modifies the method presented in Stanojević et al. [15] (doi: 10.1109/ICCCC.2016.7496752) (a).The results of our experiments showed a good performance of the sequential multiple biometric matching system based on continuous distribution approximation and optimized thresholds.(a)Reprinted (partial) and extended, with permission based on License Number3938230385072 © [2016] IEEE, from "Computers Communications and Control (ICCCC), 2016 6th International Conference on".


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How to Cite
STANOJEVIĆ,, Milan et al. Continuous Distribution Approximation and Thresholds Optimization in Serial Multi-Modal Biometric Systems. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 11, n. 5, p. 720-733, sep. 2016. ISSN 1841-9844. Available at: <>. Date accessed: 05 july 2020. doi:


multi-modal biometrics, sequential fusion, multi-criteria optimization, continuous distribution approximation