# Pgds-YOLOv8s: An Improved YOLOv8s Model for Object Detection in Fisheye Images
## 3 Materials and Methods
### The Proposed Approach
#### 3.2.2 C2 fs Module  
The exaggerated relative size and distance of objects and complex background information in fisheye images lead to further degradation of object detection performance. To further optimize object detection performance in fisheye images, the Squeeze-and-Excitation (SE) block is introduced in this paper [42]. The SE block selectively emphasizes the information features using the global information, which will pay more attention to the information channel features and effectively improve the detection performance of the objects in fisheye images. As shown in Figure 9, the SE block contains Squeeze-and-Excitation operations. First, the global average pooling in the squeeze operation processes the spatially informative features of the feature map into channel informative features to obtain the global features on the channels. This is followed by the excitation operation, which learns the nonlinear relationships between channels and captures the interdependencies between channels to recalibrate the channel features adaptively. Finally, the generated scalar is multiplied by the original feature map for feature fusion to obtain the final features. The SE block uses global information to emphasize informative features in the fisheye image selectively. It improves sensitivity to features in the fisheye image and suppresses less useful features. Figure 9: A Squeeze-and-Excitation block. The \(\mathbf{F}_{tr}\) operation generates a feature map \(\mathbf{U}\) from the input feature map \(\mathbf{X}\) with a convolution operation, where \(\mathbf{X}\in\mathbb{R}^{H^{\prime}\times W^{\prime}\times C^{\prime}}\) and \(\mathbf{U}\in\mathbb{R}^{H\times W\times C}\). \(\mathbf{F}_{sq}\) denotes the squeeze operation. The squeeze performs the global average pooling operation on the feature map to generate the channel-wise statistics \(\mathbf{z}\)[42], where \(\mathbf{z}\in\mathbb{R}^{\mathbb{C}}\), which represents the global perceptual field of each channel using a numerical value, where the equation for the \(c\)-th element of \(\mathbf{z}\) is expressed as follows:  
\[z_{c}=\mathbf{F}_{sq}(\mathbf{u}_{c})=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j =1}^{W}u_{c}(i,j) \tag{7}\]  
\(\mathbf{F}_{ex}\) denotes the excitation operation, and the excitation uses two fully connected layers to parameterize the gating mechanism and to capture channel-wise dependencies. Finally, the scalar \(\mathbf{s}\) is obtained. \(\delta\) denotes the ReLU function, and \(\sigma\) denotes the Sigmoid function. \(\mathbf{W}_{1}\in\mathbb{R}^{\frac{C}{\gamma}\times C}\), and \(\mathbf{W}_{2}\in\mathbb{R}^{C\times\frac{C}{\gamma}}\). \(r\) denotes the reduction ratio. The equation is expressed as follows:  
\[\mathbf{s}=\mathbf{F}_{ex}(\mathbf{z},\mathbf{W})=\sigma(g(\mathbf{z}, \mathbf{W}))=\sigma(\mathbf{W}_{2}\delta(\mathbf{W}_{1}\mathbf{z})) \tag{8}\]  
The \(\mathbf{F}_{scale}\) operation multiplies the scalar \(s_{c}\) with the corresponding channel of the feature map \(\mathbf{u}_{c}\) to obtain the final feature map \(\widetilde{\mathbf{x}}\), with \(\mathbf{u}_{c}\in\mathbb{R}^{H\times W}\). The equation is expressed as follows:  
\[\widetilde{\mathbf{x}}_{c}=\mathbf{F}_{scale}(\mathbf{u}_{c},s_{c})=s_{c} \cdot\mathbf{u}_{c} \tag{9}\]  
The C2f module in the original YOLOv8 model uses a gradient-splitting connection to obtain rich gradient flow information. To further enhance the model's understanding of the contextual information of fisheye images, the C2 fs module is proposed. As shown in Figure 10, the C2 fs module replaces the Bottleneck of the C2f module with the SE-Bottleneck. The SE-Bottleneck adds the SE attention mechanism to the Bottleneck. One branch first extracts the effective features using two \(3\times 3\) convolutional layers and then adaptively recalibrates the features using the SE module modeling the interdependence of the channels. The other branch is the original features. Finally, the features from these two branches are fused.