# Unsteady State Lightweight Iris Certification Based on Multi-Algorithm Parallel Integration
## 3 Lightweight Unsteady State Constrained Iris Certification
### Feature Recognition Layer
#### 3.2.1 Gabor + Hamming  
The Gabor filter expression is shown in Equation (1). \[\phi(x,y)=\frac{f_{0}^{2}}{\pi\gamma\eta}e^{(-(\frac{f_{0}^{2}}{\gamma^{2}}x_{t} ^{2}+\frac{f_{0}^{2}}{\gamma^{2}}y_{t}^{2}))}e^{(-2\pi\gamma\theta x_{r})}, \tag{1}\]  
where \(x_{r}=x\cos\theta+y\sin\theta y_{r}=-x\sin\theta+y\cos\theta\), \(f_{0}\) is the center oscillation frequency; \(\theta\) is the rotation angle of the Gabor kernel function; \(\gamma=f_{0}/\alpha;\alpha\) is the width of the Gaussian function in the \(x\) direction; \(x_{r}\) is the width of the \(x\) direction vector at the angle \(\theta\) of rotation; \(y_{r}\) is the width under the \(y\) direction vector at the angle \(\theta\) of rotation; \(\eta=f_{0}/\beta\), and \(\beta\) is the width of the Gaussian function in the \(y\) direction. If \(y=\eta=\delta/\sqrt{2\pi},\vec{k}=2\pi f_{0}e^{(j\theta)}\), and \(\vec{z}=(x,y)\), Equation (1) can be expressed as Equation (2). \[\phi(\vec{z})=\frac{1}{2\pi}\frac{\|\vec{k}\|^{2}}{g^{2}}e^{(-\frac{\vec{k}\|^ {2}\|^{2}\|^{2}}{2\sigma^{2}})}e^{(\vec{j}\vec{k}\times\vec{z})}, \tag{2}\]  
Figure 8: Six feature difference images: (**a**) Gaussian filter; (**b**) Square filter; (**c**) Median filter; (**d**) Bilateral filter; (**e**) Equalization histogram; (**f**) Laplacian of Gaussian. Figure 9: Stable feature recognition area of the same category and different category: (**a**) same category 1; (**b**) same category 2; (**c**) different category. where \(\sigma\) is the standard deviation of the Gaussian function; in this paper \(\sigma\)=2\(\pi\). To obtain the variation direction \(M\) of the Gabor filter kernel function and the oscillation amplitude \(\phi_{m,n}\) on the frequency scale \(N\) variable, Equation (2) can be shown as in Equation (3). \[\phi_{m,n}\left(\overset{\rightarrow}{z}\right)=\frac{1}{2\pi}\frac{\|k_{m,n} ^{\rightarrow}\|}{\sigma^{2}}e^{(\overset{\rightarrow}{\underset{\text{ \emph{B}}_{m,n}\rightarrow}{\rightarrow}\overset{2}{z}\overset{2}{z}})}e^{( \overset{\rightarrow}{\underset{\text{\emph{B}}_{m,n}\rightarrow}{ \rightarrow}\overset{2}{z}\overset{2}{z}})}k_{m,n}^{\rightarrow}=k_{n}e^{(i_{ \text{\emph{p}}m})},k_{n}=\frac{k_{\text{max}}}{f^{v}},\phi_{m}=\pi m/8, \tag{3}\]  
where \(k_{n}\) represents the frequency of the Gabor filter; \(k_{\text{max}}\) is the maximum frequency of the Gabor filter; \(f^{v}\) represents the frequency difference between two adjacent Gabor cores, \(v=1,2,\ldots,m\). Finally, there are a total of \(m\times n\) Gabor filters for iris feature extraction, where the frequency scale is \(m\). The direction \(\phi\) of the Gabor filter is equally divided into \(n\) parts in the interval \([0^{\circ},180^{\circ}]\). It can be seen from Equation (3) that the adjustment of the Gabor filter is determined by four parameters \(\{k_{\text{max}},f^{v},\)\(m,\)\(n\}\). In this paper, \(k_{\text{max}}=0.5\pi,f^{v}=\sqrt{2}\) (value from [32]), \(m=4\), and \(n=4\), giving a total of 16 groups of filters. The 256 \(\times\) 32-dimension iris recognition region is processed with 16 sets of Gabor filter and the processed image numbers are G\({}_{1}\) to G\({}_{16}\). Each Gabor processed image G\({}_{n}\) is equally divided into \(8\times 4\) sub-graphs of 32 \(\times\) 8 dimensions. The sub-graphs are numbered B\({}_{n\text{-}1}\)-B\({}_{n\text{-}32}\). The feature code is set by using the over-threshold judgment method. The determination threshold is set M\({}_{1}\). The average amplitude value \(T\) of each sub-graph is compared with M\({}_{1}\) (the decision threshold is calculated from the training iris library that meets the prerequisites for this paper, which is the best value for most iris certifications). If the amplitude value is smaller than or equal to M\({}_{1}\), the feature code of this sub-graph is set to 0. If the amplitude value is bigger than or equal to M\({}_{1}\), the feature code of this sub-graph is set to 1. Finally, there is a 512-bit (32 \(\times\) 16) binary feature code.