# FVR-Net: Finger Vein Recognition with Convolutional Neural Network Using Hybrid Pooling
## 3 The Proposed Model
### Network Architecture  
As shown in Figure 2, feature extraction comprises a total of five blocks, where each block entails one convolutional layer, followed by batch normalization and a rectified linear unit (ReLU) activation function, which increases the rate of convergence during training. To reduce the computational cost, subsampling layers that decrease the spatial dimension of the feature maps are introduced after each convolutional layer. Specifically, we devise a hybrid pooling layer where two types of pooling layers are utilized: 2D maxpooling and 2D average pooling. Maxpooling outputs the maximum value from the subregion of its input volume by convolving a kernel across its spatial dimension. This allows extracting a high activation value within the feature map and generates sharp features. On the other hand, the average pooling layer considers the average value of the subregion during each pooling operation. It is more generalized computation, which encourages the network to identify the complete extent of its input volume [40]. These layers, however, are not placed sequentially in the network; instead, they are placed in parallel such that the same feature map is distributed to both pooling layers. The intuition behind employing both pooling layers is that finger vein features are translational variant, and therefore, preservation of feature localization is as important as preserving the most discriminative features. The results of both pooling layers are concatenated to ensure that the global textural information of the feature maps generated by each convolutional layer is effectively feed-forwarded to the imminent layers in the network.  
A detailed depiction of the network structure for the feature extraction process is presented in Table 1. The preprocessed image with a dimension of 100 \(\times\) 300 \(\times\) 1 is fed into the network as input. The first three convolutional layers use a (5, 5) kernel size, while the remaining two layers use (3, 3). The larger kernel sizes are used to significantly increase the receptive field sizes, which improves recognition of large instances in the images. This is an important part of finger vein recognition because the width of the vein pattern is not necessarily the same throughout the image. By doing so, the network not only captures the local patterns but also the global ones that span a large area in the image. The number of channels was chosen with alternate increases and decreases between two consecutive convolutional layers, maintaining the computational complexity that might occur when large filters are used across the network. After hybrid pooling, the concatenation layers (C1-C5) are responsible for concatenating the output features of both subsampling layers  
Figure 2: The proposed FVR-Net architecture.  
before passing them to the next block. Furthermore, to prevent overfitting while training with big data, an L2 regularizer with a regularization penalty of 0.0001 is used at each convolutional layer. Because each layer processes computationally inexpensive parameters and the L2 regularizer can provide sufficient regularization [41], dropouts are not utilized.