## 2 The Proposed Method
### GHPNet Network Architecture
By adding \(1\times 1\) convolution before the \(3\times 3\) convolution of each layer, the MF module can effectively reduce the amount of network parameters and thus save the time complexity of the network. In the GHE module, we first use three convolutions to progressively refine the details of the feature map from the MF module, with channel sizes from 32 to 16. Then, two convolution layers are used consecutively to estimate the Gaussian heat value at each position. Since the values of the Gaussian map are always non-negative, we apply a ReLU activation behind the last convolution layer. Finally, GHE generates the high-resolution Gaussian heap map with the same size as the input image. Let \(\text{Get}_{\text{u,v}}^{\text{est}}\) be the estimated Gaussian heap value of v-th pixel in u-th training samples and \(\text{G}_{\text{u,v}}^{\text{gt}}\) be the corresponding ground-truth of the Gaussian heat value. Our network is trained using the \(\text{L}^{2}\) loss defined as:  
\[\text{L}=\frac{1}{\text{N}}\times\frac{1}{\text{H}\times\text{W}}\sum_{\text{ u=1}}^{\text{N}}\left(\sum_{\text{v=1}}^{\text{H}\times\text{W}}\left\|\text{G}_{ \text{u,v}}^{\text{est}}-\text{G}_{\text{u,v}}^{\text{gt}}\right\|_{2}^{2}\right) \tag{6}\]  
where N is the number of samples for batch training and \(\text{H}\times\text{W}\) is the spatial dimension of the original input image. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Network Layer** & **Parameter Setting** & **Output Dimension** & **Network Layer** & **Parameter Setting** & **Output Dimension** \\ \hline \multirow{5}{*}{Conv1\_x} & FE module & Conv7\_x & \(\left[\begin{array}{cc}1\times 1,&512\\ 3\times 3,&256\end{array}\right]\) & \(16\times 16\times 256\) \\  & \(\left[\begin{array}{cc}3\times 3,&64\\ 3\times 3,&128\end{array}\right]\) & \(128\times 128\times 64\) & Conv8\_x & \(\left[\begin{array}{cc}1\times 1,&256\\ 3\times 3,&128\end{array}\right]\) & \(32\times 32\times 128\) \\  & \(\left[\begin{array}{cc}3\times 3,&128\\ 3\times 3,&256\end{array}\right]\) & \(64\times 64\times 128\) & Conv9\_x & \(\left[\begin{array}{cc}1\times 1,&128\\ 3\times 3,&64\end{array}\right]\) & \(64\times 64\times 64\) \\  & \(\left[\begin{array}{cc}3\times 3,&256\end{array}\right]\) & \(32\times 32\times 256\) & Conv10\_x & \(\left[\begin{array}{cc}1\times 1,&64\\ 3\times 3,&32\end{array}\right]\) & \(128\times 128\times 32\) \\  & \(\left[\begin{array}{cc}3\times 3,&512\\ 3\times 3,&512\end{array}\right]\) & \(16\times 16\times 512\) & GHE module \\  & \(\left[\begin{array}{cc}3\times 3,&512\\ 3\times 3,&512\end{array}\right]\) & \(8\times 8\times 512\) & Conv11\_x & \(\left[\begin{array}{cc}3\times 3,&32\\ 3\times 3,&32\\ 3\times 3,&16\end{array}\right]\) & \(128\times 128\times 1\) \\  & \(\left[\begin{array}{cc}3\times 3,&1024\\ 1\times 1,&1024\end{array}\right]\) & \(8\times 8\times 1024\) & Conv11\_x & \(\left[\begin{array}{cc}3\times 3,&32\\ 3\times 3,&32\\ 3\times 3,&16\\ 1\times 1,&16\end{array}\right]\) & \(128\times 128\times 1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting of the GHPNet. Finally, the Gaussian heatmap is processed by calling the watershed segmentation function \(\textit{Watershed}()\) of the open source OpenCV library so as to obtain the detection results of birds in the aggregation area.