## 4 Experimental Results and Analysis
### Effect of Different Combination Methods of Sample Pairs on Performance  
This paper introduces the advantages and disadvantages of two sample pair combination methods--differential image and synthetic image--and combines their characteristics to propose the use of aligned synthetic samples as the sample pair combination method in this paper, i.e., the two samples in a sample pair are firstly aligned to find the common region, and then combined into a synthetic image as the input of the network. In this  
Figure 9: Comparison of ROC curves of optimizable models.  
section, a comparative experimental analysis of these three combination methods is carried out, and their performance is individually tested on three publicly available datasets for training. The networks are all deep tree networks as proposed in this paper, and the data are divided into training, validation, and test sets using the closed-set test approach; none of them are augmented with online data.  
Figure 10: Equivalent error rate curves of test results for different combinations of sample pairs in three publicly available datasets: (**a**) FV-USM; (**b**) MMCBNU_600; (**c**) SDUMA-HMT.  
Table 8 shows the test results of different combinations of sample pairs on the three public datasets, and Figure 5 shows the corresponding equal error rate curves (the legend \"composite\" corresponds to \"synthetic image\", while \"difference\" corresponds to \"composite image\" and \"difference\" in the table). The legend \"composite\" corresponds to \"composite image\", \"difference\" corresponds to \"difference image\", and \"align + difference\" corresponds to \"align + difference\" (align + difference\" corresponds to \"align + composite\" in the table).  
As can be seen from Table 9, the aligned synthetic samples proposed in this paper outperform the two sample pair combination methods of differential and synthetic images on all three datasets under the same network structure and datasets, exhibiting a great improvement. When comparing the fourth and fifth rows of the table to the second and fifth rows, respectively, it can be seen that the performance is improved after adding the alignment method to both the original differential and synthetic images, which verifies the effectiveness of the alignment method used in this paper against the vein pattern shift. Meanwhile, the comparison of the specific values in the third and fifth rows of the table shows that the proposed aligned synthetic image has the most obvious effect on SDUMA-HMT, followed by MMCBNU_6000, and the least improvement on FV-USM. The alignment of the original data greatly improves the vein offset due to finger rotation between the intraclass samples, but has less improvement on the light and dark samples. The improvement is small for the difference between light and dark, due to different illumination, and the most severe grain shift is found in SDUMA-HMT, but the difference between light and dark between samples is very small, so the improvement is the largest after adding the alignment method. In FV-USM, except for a small number of samples with grain offset, there are large differences between the samples of all fingers, despite it being a closed-set test, because the division method in this paper first randomly forms sample pairs and disrupts them, and then randomly divides them into training, validation, and test sets proportionally, which increases the difficulty of the test to some extent. Therefore, the alignment-only method has less improvement in illumination, and the performance improvement on FV-USM is relatively small.