# Person Search via Deep Integrated Networks
## 3 Overview of the Deep Integrated Networks for Person Search
### Pedestrian Detection Network
#### 3.1.1 Sharing Convolutional Layers  
The Zeiler and Fergus model [65] is a CNN which comprises five sharing convolutional layers with the corresponding rectified linear unit (ReLU) layer, two pooling layers and two local response normalizations (LRN) [16] which was applied in the proposed configuration. In the convolutional layers, the convolution operations are performed on the input with multiple kernels, each of which is also called a filter and refers to a rectangular array. Assuming the input size to the \(l\)-th layer is \(H^{l}\times W^{l}\times D^{l}\) and the size of the \(d\)-th kernel \(f^{d}\) is \(H\times W\times D^{l}\), the convolution results, which are called feature maps, have the size of \(\left(H^{l}-H+1\right)\times\left(W^{l}-W+1\right)\times D\) and \(D\) is the number of kernels. In mathematics, the convolution result \(y\) at the spatial location \(\left(\hat{x}^{l+1},\hat{y}^{l+1}\right)\) in the \(d\)-th feature map can be represented as  
\[y_{\hat{x}^{l+1},\hat{y}^{l+1},d}=\sum_{m=0}^{H}\sum_{n=0}^{W}\sum_{\hat{x}^{l} =0}^{D^{l}}f^{d}_{m,n,d}\times x^{l}_{\hat{x}^{l+1}+m,\hat{y}^{l+1}+n,d} \tag{1}\]  
where \(x^{l}\in\Re^{H^{l}\times W^{l}\times D^{l}}\) is the input to the \(l\)-th layer, \(x^{l}_{\hat{x}^{l+1}+m,\hat{y}^{l+1}+n,d}\) is the element of \(x^{l}\) at the location \(\left(\hat{x}^{l+1}+m,\hat{y}^{l+1}+n,d\right)\)\(0\leq\hat{y}^{l+1}<H^{l}-H+1\), \(0\leq\hat{y}^{l+1}<W^{l}-W+1\), and \(0\leq d<D=D^{l+1}\). Note that the stride--the number of pixels a convolutional kernel moves across an image space--is 1 and no zero padding is used to pad the input with zeros around the border. The ReLU layer does not change the size of the input. In other words, the size of \(x^{l}\) and \(y\) is the same. ReLU is an active function which is performed individually for every element in the input \(x^{l}\) and it is formulated as [66]  
\[y_{i,j,d}=max\Big{\{}0,x^{l}_{i,j,d}\Big{\}} \tag{2}\]  
where \(0\leq i<H^{l}=H^{l+1}\), \(0\leq j<W^{l}=W^{l+1}\), and \(0\leq d<D=D^{l+1}\).  
Two types of pooling operators are widely used: max pooling and average pooling [66]. The max pooling operation is performed on each subregion of \(3\times 3\) or \(5\times 5\) pixels and the maximum value within a subregion is preserved, while the average pooling operation is used to preserve the averaging values within a subregion. Hence, the pooling operation requires no parameter. Assume the stride in the vertical and horizontal direction are \(P\) and \(Q\), respectively; the output size of the pooling layer will be \(H^{l+1}\times W^{l+1}\times D^{l+1}\), where \(H^{l+1}=\frac{H^{l+1}}{P}\), \(W^{l+1}=\frac{W^{l+1}}{Q},D^{l+1}=D^{l}\), and it can be formulated as  
\[y_{\hat{x}^{l+1},\hat{y}^{l+1},d}=\underset{0\leq p<P,0\leq q<Q}{max}x^{l}_{ \hat{x}^{l}(l+1)\hat{x}^{l}+p,\hat{y}^{(l+1)\hat{x}^{l}+W}+q\hat{x}^{l}} \tag{3}\]  
where \(0\leq\hat{x}^{l+1}<H^{l+1}\), \(0\leq\hat{y}^{l+1}<W^{l+1}\), and \(0\leq d<D^{l+1}=D^{l}\).  
Figure 2: Configuration of the pedestrian detection network composed of three parts: sharing convolutional layers, region proposal network and region of interest (ROI) pooling and classification layers. LRN: local response normalization; ReLU: rectified linear unit; FC: fully-connected layer.  
The network configuration is shown in Table 1. When inputting an image frame with an arbitrary size, this would be resized to \(563\times 1000\) pixels. The size of the feature maps output by the fifth convolution layer was \(36\times 64\times 256\) pixels. More details of the network parameters are presented in Section 4.