# Cancelable Multimodal Biometrics Based on Chaotic Maps
## 4 Experimentation Results
### Performance Analysis  
In this experimentation, the _FVC2002_ standard procedure was used to generate the legitimate (genuine) and illegitimate (impostor) scores. The impostor score was created by matching the first image of each subject with the corresponding first image of every other subject, whereas the genuine score is generated by matching each image with all the other images from the same subject. Hence, a verification system can be considered as a binary classification problem as follows. For a user (U) with a claimed identity \(I\) and a query feature set \(F_{Q}\), we need to determine whether the user belongs to the genuine or impostor class. Considering the fact that \(F_{I}\) is the stored template assigned to the identity \(I\), a matching score \(S\), which compares \(F_{Q}\) and \(F_{I}\), is computed. The verification system then provides a decision by comparing the matching score \(S\) to a pre-defined threshold \(\epsilon\). A large score indicates a good match, which means that the user is genuine. The decision rule is expressed as  
\[U_{(I,F_{Q})}\in\left\{\begin{aligned} & genuine,\quad if \quad S\geq\epsilon\\ & impostor,\quad if\quad S<\epsilon\end{aligned}\right. \tag{7}\]  
The recognition rate of the multimodal approach was computed using the score-level fusion of the fingerprint and face biometrics based on the weighted sum rule [26]. Moreover, 0.3 and 0.7 were acquired as weights to fingerprint and face scores, respectively. However, normalization is necessary before the fusion process because the scores generated by the diverse systems and algorithms in each constituent process are inherently dissimilar. Since matching in multimodal techniques is influenced by the normalization procedure, efficacy and resilience are the two key criteria to be considered for choosing the most appropriate method. Hence, the performance-anchored normalization (PAN) technique,  
Figure 2: Proposed cancelable approach architecture (authentication stage).  
which is improved min-max normalization, was utilized in this study to fuse the scores obtained from each matching module [24].  
Figure 3 illustrates the genuine and impostor matching score distribution (the term \"distribution\" refers to a histogram). Better discriminability between genuine and impostor users was achieved in this experiment since the corresponding distributions are well separated at a threshold equal to 0.4593--as shown in the figure.  
To confirm the efficacy of the proposed approach, the false acceptance rate (FAR) and the false rejection rate (FRR) were computed. FRR denotes the proportion of genuine scores that are smaller than the pre-defined threshold \(\epsilon\) (\(FRR=p(S<\epsilon|genuine)\)), and FAR denotes the fraction of impostor scores that are larger than or equal to \(\epsilon\) (\(FAR=p(S\geq\epsilon|impostor)\)). Figure 4 shows that the equal error rate (EER)--which is the point at which the FAR and FRR are equal--of the proposed scheme is 0% when the threshold is 0.4593.  
Figure 4: The EER of the proposed multimodal cancelable approach.  
Figure 3: The matching distribution of genuine and impostor scores.  
To validate the effectiveness of the multimodal fingerprint-face system in comparison with the unimodal face and fingerprint systems, the receiver operating curve (ROC) is shown in Figure 5. The ROC is used to relate the genuine acceptance rate (GAR) against the FAR at different threshold values. The GAR can be defined as the fraction of genuine scores that are larger than \(\epsilon\) (\(GAR=1-FRR\)). As depicted in Figure 5, the GAR of the unimodal system based on the fingerprint is equal to 95.58% at an FAR of 0.05%. The corresponding GAR value of the unimodal system based on face and the proposed multimodal approach is 100%. Hence, it was concluded that the proposed approach can maintain the highest performance while encountering the major shortcoming of unimodal biometric authentication approaches.