## 4 Proposed Method
### Pre-Processing of Data
#### 4.1.3 MCNN Feature Extraction  
In this work, N number of convolutional neural networks with different retinal sizes (i.e., the size of the retina corresponds to the size of the input images). A given input image is resized N times to the retina in each network. The issue of optimization of classifier outputs is a recurring issue in the field of pattern recognition. For the recognition of iris, it has been shown [46] that a simple averaging of the outputs of each classifier makes it possible to obtain classification rates at least as good as with a linearly combined weights that can be learned via a cross validation method [47]. As the classifiers act at the same resolution [46], so there is no reason to weight them and also these classifiers are differ from each other in terms of input distortions. In this work, we assume that the classifier with the lowest resolution are not as important as the one with the highest resolution. The final results are therefore calculated based on the linearly combined N CNNs classifiers. Figure 5 shows the overall architecture of MCNN proposed in this work.  
We build 4 CNNs acting at different resolutions. Here, we keep the size of the images with the resolution of 80 \(\times\) 80. Which is then divided by a factor \(\sqrt{2}\), \(\sqrt[3]{2}\), \(\sqrt[3]{2}\) according to each axis to obtain respective images of size 56 \(\times\) 56, 40 \(\times\) 40 and 28 \(\times\) 28. The networks called \(CNN_{80}\), \(CNN_{56}\), \(CNN_{40}\)  
Figure 4: Normalized iris image.  
Figure 5: The global architecture of the multi-scale convolutional neural network (MCNN).  
Figure 3: [PERSON]’s Rubber sheet model for the normalization of the iris.  
and \(CNN_{28}\) are built similar to the LeNet model [35] and contain different sizes of the convolution kernel and retina. In our recognition system, we use 6 layers to make the extraction of characteristics for each CNN (Figure 6, Table 1) as follows:  
* **Layer to enter**: A picture size 28 \(\times\) 28;
* **First convolution layer**: Number of convolution kernel (filters) is 6 of Size 5 \(\times\) 5; the result is a set of 24 \(\times\) 24 convolutional maps;
* **Subsampling layer**: number of maps is 6; kernel size: 2 \(\times\) 2; Size of the maps: 12 \(\times\) 12;
* **Second convolution layer**: Number of convolution kernel (filters) is 6 of Size 5 \(\times\) 5; the result is a set of 8 \(\times\) 8 convolutional maps;
* **Subsampling layer**: number of maps: 6; kernel size: 2 \(\times\) 2; Size of maps: 4 \(\times\) 4;
* **Third convolution layer**: Number of convolution kernel (filters) is 6 of Size 4 \(\times\) 4; the result is a set of 1 \(\times\) 1 convolutional maps.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \(CNN_{80}\) & \(CNN_{56}\) & \(CNN_{40}\) & \(CNN_{28}\) \\ \hline
**Layer** & **Type** & **80\(\times\)80** & **56\(\times\)56** & **40\(\times\)40** & **28\(\times\)28** \\ \hline C1 & Convolution & & 7\(\times\)7 & 7\(\times\)7 & 5\(\times\)5 & 5\(\times\)5 \\  & & 74\(\times\)74 & 50\(\times\)50 & 36\(\times\)36 & 24\(\times\)24 \\ \hline P2 & Max-pooling & & 2\(\times\)2 & 2\(\times\)2 & 2\(\times\)2 & 2\(\times\)2 \\  & & 37\(\times\)37 & 25\(\times\)25 & 18\(\times\)18 & 12\(\times\)12 \\ \hline C3 & Convolution & & 6\(\times\)6 & 6\(\times\)5 & 5\(\times\)5 & 5\(\times\)5 \\  & & 32\(\times\)32 & 20\(\times\)20 & 14\(\times\)14 & 8\(\times\)8 \\ \hline P4 & Max-pooling & & 4\(\times\)4 & 4\(\times\)4 & 2\(\times\)2 & 2\(\times\)2 \\  & & 8\(\times\)8 & 5\(\times\)5 & 7\(\times\)7 & 4\(\times\)4 \\ \hline C5 & Convolution & & 1\(\times\)1 & 1\(\times\)1 & 1\(\times\)1 & 1\(\times\)1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Network architectures in each box of the table; Top: size of the segmented eye image and Bottom: size of the map.  
Figure 6: Example of Extraction phase by CNN.  
After the extraction, classification is performed to classify the images. Here, output in the last layer gives one neuron per class (each neuron represents a class of eyes of each person) (Figure 7).