## 4 Experimental Results
### Vein Pattern Recognition Based on Combined Features  
Our human recognition is based on hybrid features that combined geometric-related features and vein pattern features. The geometric features are related to the geometric structure of the hand, namely the geometric error (E\({}_{\text{Hand}}\)) derived from Equation (12). The vein pattern features are the vein pattern error (E\({}_{\text{VeinMap}}\)) and barcoded features error (E\({}_{\text{Vein}}\)) derived from Equations (11) and (13), respectively.  
Figure 25: Ten randomly selected vein images in the query set aligned against each of the corresponding ten reference vein images. Images on the diagonal are perfectly matched.  
The combined error is the weighted linear combination of these errors (Equation (14)), which is then used in our vein pattern human recognition system.  
We have tested the performance of our vein pattern recognition system on 140 subjects (87 females; 53 males) with an age between 18 and 40 years. Ten images are collected from one subject with different hand orientations, including a left and right roll rotation, front and back pitch rotation, left and right yaw rotation and four relaxed hand positions. The roll, pitch and yaw rotation collection are shown in Figure 26.  
The limits of the roll and pitch angles are within \(\pm 20\), while that of the yaw angle is 0-180\({}^{\circ}\). The total number of images is 1400 (140 \(\times\) 10) images. The number of genuine matches is 6300 matches (45 possible pairs of vein patterns coming from the same hand \(\times\) 140 individuals = 6300) and the number of impostor matches is 9730 matches ((140 \(\times\) 139/2) possible pairs of template vein patterns coming from the different vein patterns). The distribution of matching scores is generated in a set of two parallel images--images obtained from the same hand (red line on the right) and the ones from different hands (blue line on the left), as shown in Figure 27, where the cross-over point of the false non match rate (FNMR) curve and the false match rate (FMR) curve is 0.607.  
As shown in Figure 28, we calculated the Receiver Operating Characteristics (ROC) curve. The area under the curve (AUC) is used as the optimization objective since it provides a good representation of the ROC performance. In this system, the AUC value of 0.99842 shows that our method is extremely good. We also evaluated the overall performance in terms of equal error rate (EER), known as the error rate when the false non match rate (FNMR) of genuine vein patterns and the false match rate (FMR) of impostor vein patterns assume the same value, as shown in Figure 29. A common approach is to use the cross-over point between the FNMR curve and the FMR curve. In this regard, we have achieved an EER of 0.243%, indicating that our method is feasible and effective for dorsal vein recognition with a high accuracy. Finally, a detection-error tradeoff (DET) curve plotting the FMR against the FNMR is presented in Figure 30. The comparison results are presented in Table 2.  
Figure 26: vein pattern impressions of (**a**) and (**c**) row angle, (**b**) and (**d**) pitch angle, (**e**) and (**f**) yaw angle.  
Figure 28: Zoomed-in Receiver Operating Characteristics (ROC) curve, where the square mark in the circle represents the cut-off point.  
Figure 27: Distribution of genuine similarity score and distribution of impostor similarity score.  
Figure 29: False match rate (FMR) and false non-match rate (FNMR) curves.