## 4 Experimental Results
### Evaluation of Feature Extraction and Matching Modules
#### 4.3.3 Equal Error Rate  
The equal error rate (EER) corresponds to the error rate for which (1- GAR) and FAR are equal. To verify the effectiveness of our model, we compared it with the state-of-the-art hand-crafted methods in terms of EER as the performance indicator. These methods included the principal line (PriLine) [30], competitive code (CompCode) [31], double orientation code (DOC) [32], extended binary orientation co-occurrence vector (E-BOCV) [33], local line directional patterns-modified finite radon transform (LLDP-MRAT) [34], and local line directional patterns-Gabor (LLDP-Gabor) [34] described in Section 2.2. Table 4 presents EER results of the aforementioned methods and our proposed model in the verification task for the contact-based HKPU database. To avoid presenting a large table, we report only more recent state-of-the-art methods demonstrated to outperform old ones in our results. It should be pointed out that the verification performance of each algorithm was obtained by matching palmprints from different sessions. In fact, the images related to the first session were used as the training set and the images related to the second session were considered as the test set. We also performed verification experiments for the IITD touchless database. The EERs obtained using different methods are summarized in Table 5. In the experimental results, the training set included the first four images and the remaining images were utilized as the test set. According to Tables 4 and 5, the results corroborate that using the linear SVM classifier in our matching module with the input of extracted deep features achieved the best performance in terms of the EER value among the state-of-the-art methods, which can be attributed to discriminative deeply learned features. In the other words, the CNN features extracted by our model were highly dominating over the only line features in PriLine and the orientation-based features in coding methods, so it can address the shortcomings of hand-crafted features. Moreover, as local feature-based methods, hand-crafted approaches generally demand more high-resolution palmprint images and have slower matching speed than our proposed model. Although LLPD-based methods have shown good performance as palmprint texture descriptors, they suffer from computation complexity and slower matching speed. Furthermore, we can see from the comparative results that the overall EER rate for contact-based HKPU database was higher than that of the IITD touchless database because illumination, distortion, translation, and rotation variances in contact-less palmprint images led to less-significant features. Since our proposed model was tested on two palmprint image databases, we are fairly confident about the generalizability of our model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**PriLine**} & \multirow{2}{*}{**CompCode**} & \multirow{2}{*}{**DOC**} & \multirow{2}{*}{**E-BOCV**} & \multicolumn{3}{c}{**Classifier in Our Proposed Model**} \\ \cline{5-6}  & & & & & **SVM** & **KNN** & **RF** \\ \hline EER (\%) & 0.133 & 0.026 & 0.019 & 0.053 & 0.0125 & 0.0156 & 0.0625 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison with state-of-the-art methods in terms of EER value for the contact-based HKPU database. CompCode: competitive code; DOC: double orientation code; E-BOCV: extended binary orientation co-occurrence vector; PriLine: principal line. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**CompCode**} & \multirow{2}{*}{**DOC**} & \multirow{2}{*}{**LLPD-MRFT**} & \multirow{2}{*}{**LLPD-Gabor**} & \multicolumn{3}{c}{**Classifier in Our Proposed Model**} \\ \cline{5-6}  & & & & & **SVM** & **KNN** & **RF** \\ \hline EER (\%) & 0.101 & 0.062 & 0.031 & 0.028 & 0.0276 & 0.0328 & 0.0889 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison with state-of-the-art methods in terms of EER value for the IITD touchless database.