# Optimized Score Level Fusion for Multi-Instance Finger Vein Recognition
## 5 Experimental Analysis
### Performance Analysis of Multi-Instance Feature Descriptors Biometrics  
The proposed system uses the Bayesian optimization approach to search for an optimal set of hyperparameters of the histogram of oriented gradients (HOG). The hyperparameters are: _orientations_, _pixels_, _cells_, _norm_, and _transform_sqrt_. _Orientations_ is the number of orientations. _Pixels_ is the number of pixels in a cell, while _Cells_ is the number of cells in a HOG block. _Norm_ is the type of block normalization being used, and _Transform_sqrt_ indicates whether the power-law compression is being used to normalize the image before processing. For optimization purposes, the _orientations_ hyperparameter is set in the range of four to twenty. The _pixels_ hyperparameter is set in the range of eight to thirty. The _cells_ hyperparameter is set in the range of one to four. The _norm_ hyperparameter is set for either L1, L1-sqrt, L2, or L2-Hys. On the other hand, the _transform_sqrt_ hyperparameter is set to Yes or No. Figure 6 depicts the parallel coordinates plot of the hyperparameters. The figure shows the overview of the hyperparameters that give optimal results. The figure consists of all the hyperparameter optimization trials by the Bayesian optimizer for all fingers, datasets, and matchers. Overall, it could be observed that most _orientations_ hyperparameter values, and most _cells_ hyperparameter values are in the range of one to three, whereas L2 and  
Figure 5: The sample images of UTFVP Finger Vein Dataset. L1-sqrt _norm_, without _transform_sqrt_, and high _pixels_ hyperparameter values in the range of twenty-six to twenty-nine are optimal. The experimental results of the proposed methods for SDUMLA-HMT are presented in Table 1. The ROC curve of the proposed system for SDUMLA-HMT is illustrated in Figure 7. For the UTFVP dataset, the experimental results of the proposed method can be seen in Table 2, while the ROC curve of the proposed system for UTFVP is depicted in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Fingers** & **Matchers** & **Orientations** & **Pixels** & **Cells** & **Norm** & **Transform\_sqrt** & **EER** \\ \hline ('li’,) & BSBF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 17.45\% \\ ('li’,) & BSBF-linear2 & 15 & 30 & 2 & L2-Hys & No & 12.85\% \\ ('li’,) & BSBF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 17.45\% \\ ('li’,) & BSBF-rbf2 & 9 & 29 & 2 & L2-Hys & No & 12.77\% \\ ('li’,) & BSSF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 2.71\% \\ ('li’,) & BSSF-linear2 & 16 & 26 & 2 & L1-sqrt & Yes & 1.57\% \\ ('li’,) & BSSF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 2.71\% \\ ('li’,) & BSSF-rbf2 & 18 & 26 & 2 & L2-Hys & Yes & 1.35\% \\ ('li’, 'lm’) & BSBF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 14.78\% \\ ('li’, 'lm’) & BSBF-linear2 & 13 & 27 & 3 & L2-Hys & No & 11.85\% \\ ('li’, 'lm’) & BSBF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 14.15\% \\ ('li’, 'lm’) & BSBF-rbf2 & 19 & 29 & 2 & L2-Hys & No & 9.60\% \\ ('li’, 'lm’) & BSSF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 1.10\% \\ ('li’, 'lm’) & BSSF-linear2 & 14 & 8 & 1 & L1 & Yes & 0.58\% \\ ('li’, 'lm’) & BSSF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 1.10\% \\ ('li’, 'lm’) & BSSF-rbf2 & 7 & 26 & 2 & L2-Hys & No & 0.77\% \\ ('li’, 'lm’, 'lr’) & BSBF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 12.22\% \\ ('li’, 'lm', 'lr') & BSBF-linear2 & 17 & 28 & 1 & L2 & No & 9.80\% \\ ('li’, 'lm', 'lr') & BSBF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 10.94\% \\ ('li’, 'lm', 'lr') & BSBF-rbf2 & 16 & 26 & 1 & L2 & No & 6.44\% \\ ('li’, 'lm’, 'lr') & BSSF-linear1 & 9 & 8 & 3 & L2-Hys & Yes & 0.68\% \\ ('li’, 'lm', 'lr') & BSSF-linear2 & 8 & 15 & 1 & L2-Hys & No & 0.56\% \\ ('li’, 'lm', 'lr') & BSSF-rbf1 & 9 & 8 & 3 & L2-Hys & Yes & 0.56\% \\ ('li’, 'lm', 'lr') & BSSF-rbf2 & 10 & 17 & 1 & L2 & Yes & 0.48\% \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental results of the proposed system for SDUMLA-HMT. Figure 6: Parallel Coordinates Plot of the Hyperparameters.