# Discriminative Local Feature for Hyperspectral Hand Biometrics by Adjusting Image Acutance
## 3 Experiments
### Experimental Analysis  
To investigate why hyperspectral hand databases performed better after acutance adjustment. We assumed that the distance of the local features for an individual's same hand is decreased, while for different people their hand distance is increased when the acutance of the database is adjusted to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Local Pattern** & **Band** & **Optimal Range (\(t_{1}\)–\(t_{2}\))** & **RR 1 (On Optimal Range)** & **RR (Original Image)** & **Improvement** \\ \hline \multirow{4}{*}{HDHV} & \multirow{2}{*}{Reginal LBP} & 890 nm & 3.515-6.412 & 0.9833 & 0.9583 & 2.6\% \\  & & All & - & 0.9540 & 0.7365 & **29.5**\% \\ \cline{2-6}  & \multirow{2}{*}{Deep feature} & 890 nm & 3.515-6.412 & 0.9750 & 0.9542 & 2.2\% \\  & & All & - & 0.8266 & 0.6154 & 36.9\% \\ \hline \multirow{4}{*}{HPV} & \multirow{2}{*}{CompCode} & 900 nm & 4.865-6.237 & 0.9928 & 0.7919 & 25.3\% \\  & & All & - & 0.8964 & 0.6152 & **45.7**\% \\ \cline{2-6}  & \multirow{2}{*}{Deep feature} & 900 nm & 4.865-6.237 & 0.9809 & 0.7895 & 24.2\% \\ \cline{1-1}  & & All & - & 0.7317 & 0.4414 & 65.7\% \\ \hline \hline \end{tabular}  
* The best result in the optimal range.  
\end{table} 
Table 1: Results on representative spectral from the hyperspectral databases. Figure 14: Recognition rates (RR) with different acutance TPVA on the green band of HPV with different local texture patterns. Results using the feature extraction methods of (**a**) CompCode; (**b**) deep features. Figure 13: Recognition rates (RR) with different acutance (corresponding to 8) for every band (spectrum) of HPV using different local texture patterns. Results using the feature extraction methods of (**a**) CompCode; (**b**) deep features. the optimal range. To this end, one evaluation method which is inspired by the Fisher criterion [48], was used to measure the discrimination of the features extracted from the database (after actance adjustment). The \(r\) with respect to the ratio of within-class variance to between-class variance is introduced as follows:  
\[r=\frac{1}{D}\sum_{d=1}^{D}\left(\frac{v_{w}^{d}}{v_{b}^{d}}\right)^{2} \tag{8}\]  
where  
\[v_{w}^{d}=\sum_{k=1}^{K}\sum_{n\in C_{k}}\left(x_{n}^{d}-m_{k}^{d}\right)^{2}~ {}~{}m_{k}^{d}=\frac{1}{N_{k}}\sum_{n\in C_{k}}x_{n}^{d} \tag{9}\]  
\[v_{b}^{d}=\sum_{k=1}^{K}N_{k}\left(m_{k}^{d}-m^{d}\right)^{2}~{}~{}m^{d}=\frac {1}{N}\sum_{n=1}^{N}x_{n}^{d} \tag{10}\]  
The notations are detailed below:  
\(v_{w}^{d}\): the within-class variance for the \(d_{th}\) feature of the \(D\) features. \(v_{b}^{d}\): the between-class variance for the \(d_{th}\) feature of the \(D\) features. \(x_{n}^{d}\): the \(d_{th}\) feature of the \(n_{th}\) sample in the database containing \(N\) samples. \(C_{k}\): the \(k_{th}\) class in the database consisting of \(K\) classes. \(N_{k}\): the number of samples belonging to the \(k_{th}\) class. The best performing band in the identification phase from the hyperspectral (HDHV--890 nm and HPV--900 nm) hand databases was chosen for analysis. Based on the local features extracted from these databases, the \(r\) values were calculated via Equation (8), where a smaller \(r\) value signifies a more discriminative local feature. Figure 15 depicts that after being convolved with different Gaussian filters, the \(r\) value first decreased and then increased, which indicates that the local features have the most discrimination in the optimal actance range obtained from the previous subsection (see Table 2). Therefore, by adjusting image actance, the local feature from the hyperspectral and multispectral hand databases become discriminative resulting in a better performance.