# Individuals Identification Based on Palm Vein Matching under a Parallel Environment
## 5 Results
### Experimentation in Verification Mode  
In this mode, a set of matching scores are obtained for intra-class and inter-class comparisons. Consequently, Table 3 shows the number of intra-class and inter-class matching pairs on each dataset, together to its description, respectively.  
Figure 7 shows the distributions of genuine and imposter matching scores of the proposed method on different databases. Matching scores for the three datasets present a slightly similar distribution. There is an overlap for genuine and imposter matching scores. However, it is noticeable that scores for imposter matching are denser and closer to 0. In addition, both distributions are separable for all databases, which suggests that the CPM is able to find similarities for similar palm vein images while distinguishing image samples from different fingers.  
The accuracy of our method is examined by computing the EER (equal error rate), FRR (false rejection rate) at-zero-FAR (false acceptance rate), and FAR at-zero-FRR. Table 4 shows the results on different datasets, while Figure 8 depicts the ROC curves obtained for FAR and FRR results on the databases.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Database** & **Intra-Class Comparisons** & **Inter-Class Comparisons** \\ \hline CASIA-MS-PalmprintV1 & 3000 & 1,432,800 \\  & (100 _persons_\(\times\) 2 _hands_\(\times\)\(C_{6}^{2}\)) & (100 _persons_\(\times\) 2 _hands_\(\times\) 6 _samples_) \\  & & \(\times\)199 _different hands_\(\times\) 6 _samples_) \\ \hline VERA Palm vein & 9900 & 4,818,000 \\  & (110 _persons_\(\times\) 2 _hands_\(\times\)\(C_{10}^{2}\)) & (110 _persons_\(\times\) 2 _hands_\(\times\) 10 _samples_ \\  & & \(\times\)219 _different hands_\(\times\) 10 _samples_) \\ \hline PUT Vein & 6600 & 1,425,600 \\  & (50 _persons_\(\times\) 2 _hands_\(\times\)\(C_{12}^{2}\)) & (50 _persons_\(\times\) 2 _hands_\(\times\) 12 _samples_ \\  & & \(\times\)99 _different hands_\(\times\) 12 _samples_) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Number of intra-class and inter-class matching pairs for the experiments in verification mode on each database.  
Figure 7: Distribution of matching scores on database: (**a**) CASIA-MS-PalmprintV1; (**b**) VERA Palm vein; and (**c**) PUT Vein.  
The results of FAR and FRR plotted on the ROC curves, see Figure 8, ensure the high accuracy of the proposed method, which is also evident in Table 4. The EERs of the proposed method are under 1% for all reported databases. Previous values demonstrate the effectiveness of our proposal. Furthermore, the results of FRR at-zero-FAR are very low in the three cases, the FAR at-zero-FRR being very close to 1 for CASIA-MS-PalmprintV1 and VERA Palm vein database. These values give us a better interpretation of the performance when either no impostor or no genuine palm vein exemplar is mismatched, respectively.  
Experimental results demonstrate the effectiveness of CPM as a matching method for palm vein recognition in verification mode. However, our proposal aims to provide an alternative to calculate the displacement between palm vein images to be capable of using a large database. In this sense, the experimental results for verification task prove that sparse matching, particularly the CPM, is a good alternative to the dense matching process proposed in [45] for finger-vein recognition, which is a time-consuming algorithm. In order to reaffirm the above, Section 5.3 analyzes the performance in terms of execution time and Section 5.5 compares the proposed method against the state-of-the-art approaches.