# Unsteady State Lightweight Iris Certification Based on Multi-Algorithm Parallel Integration
## 3 Lightweight Unsteady State Constrained Iris Certification
### Feature Recognition Layer
#### 3.2.2 Haar + BP  
The high-frequency coefficients of the first-layer low-frequency sub-blocks after Haar wavelet processing are extracted from the three sub-blocks G1, G2, G3. These are the wavelet coefficient matrix of the first layer low-frequency sub-blocks after image decomposition. G1  
the feature value of each sub-block. This meant a total of 12 feature values. The Haar wavelet and the block of each sub-block are shown in Figure 10.  
According to the classification of the data, the neural network is designed to use a three-layer neural network, and the number of nodes for G1, G2, and G3 is 12, 4, and 1, respectively. The excitation function is a sigmoid function [34]. The value of connection weights is either 1 or 0, which only serves to transfer data. In Figure 12, the solid line represents the connection weight as 1, and the dotted line represents the connection weight as 0. The input layer is the absolute value of the difference of iris features between the test iris and the template iris, the sub-blocks of the same sequence number in G1, G2, and G3 are added, and the values are input into the hidden layer. The neural network structure is shown in Figure 11.  
Figure 11: Neural network structure. Figure 10: Haar wavelet and the block of each sub-blocks: (**a**) Haar wavelet; (**b**) Sub-block distribution of G1; (**c**) Sub-block distribution of G2; (**d**) Sub-block distribution of G3. The hidden layer input value is shown in Equation (5). \[X_{i}=|\text{CG1}-\hat{i}|+|\text{CG2}-\hat{i}|+|\text{CG3}-i|\quad i=1,2,3,4\enspace, \tag{5}\]  
where \(X_{i}\) is the input value of the \(i\)-th hidden layer node. \(\text{CG1}_{i}\) is the difference between \(\text{G1}-i\) of the test iris and \(\text{G1}-i\) of the template iris; \(\text{CG2}_{i}\) is the difference between \(\text{G2}-i\) of the test iris and \(\text{G2}-i\) of the template iris. \(\text{CG3}_{i}\) is the difference between \(\text{G3}-i\) of the test iris and \(\text{G3}-i\) of the template iris. The input layer output values are input to the hidden layer. The hidden layer output value \(S_{i}\) is shown in Equation (6). \[ \begin{cases}S_{i}=\frac{1}{1+e^{-D_{1}xX_{i}}}&X_{i}>M\\ S_{i}=\frac{1}{1+e^{-D_{2}xX_{i}}}&X_{i}\leq M\end{cases} . \tag{6}\]  
The stable texture features of the same category of iris are similar; therefore, the value of each iris feature difference will be small. According to the nature of the Sigmoid function, the smaller the input, the greater the output. For this reason, in order to expand the difference between irises of the same category and irises of different categories, threshold weights are set for the input of the hidden layer. The input value of the hidden layer is compared with the threshold \(M\). If the value of \(X_{i}\) is greater than \(M\) is multiplied by the threshold weight \(D_{1}\)(\(D_{1}\)\(>\)1), making the value of \(-D_{1}\times X_{i}\) closer to negative infinity, the closer the hidden layer output value \(S_{i}\) of the \(i\)-th hidden layer node is to 1; if the value \(X_{i}\) is less than or equal to \(M\) multiplied by the threshold weight \(D_{2}\)(\(D_{2}\)\(<\)1), making the value of \(-D_{2}\times X_{i}\) closer to positive infinity, the closer the hidden layer output value is to 0. In turn, the distinguishing of the hidden layer output can be improved. Finally, the hidden layer output value is input to the output layer. The input value Z of the output layer is shown in Equation (7). \[Z=\sum_{i=1}^{4}S_{i}-\frac{1-Sgn(S_{i}-F)}{4}-4. \tag{7}\]  
Because the input values of the hidden layer are all positive, the output values \(S_{i}\) of the hidden layer are all greater than 0.5, and the output values of the different iris categories of the hidden layer are smaller. Therefore, in order to increase the difference between irises of the same category and irises of different categories, threshold \(F\) is set.