## 2 Materials and Methods
### Structure of the CER-YOLOv5s Model
#### 2.2.2 E-BiFPN Feature Pyramid Network  
The YOLOv5s model uses a traditional FPN [11] + PAN [12] feature pyramid structure to handle multi-scale object detection. This structure employs a pair of top-down and bottom-up pathways to merge information at different levels. Although this simple addition approach improves the model's feature fusion capability to some extent, it overlooks the importance differences of feature maps with different resolutions during the fusion process, resulting in limited utilization of multi-scale features and restricting detection accuracy. To address this issue, this study combined the ECA [13] module with the BiFPN [14] feature fusion network to develop the proposed E-BiFPN (efficient bidirectional feature pyramid network). Its structure is shown in Figure 8.  
Figure 6: Thermal map visualization results: (**a**) original image; (**b**) regular heatmap; (**c**) CBAM heatmap.  
Figure 7: CGC3 module structure.  
Firstly, the intermediate nodes with single input and no feature fusion were removed, and skip connections were added between the same levels to retain information from the original input feature layers. The weighted fusion mechanism combines channel attention and fast normalization to adjust the contribution of feature maps at different scales. Equation (2) shows the method of fast normalization for feature fusion.  
\[O=\sum_{i}\frac{w_{i}}{\varepsilon+\sum_{j}w_{j}}.I_{i} \tag{2}\]  
where \(I_{i}\) represents the input feature; \(O\) represents the output feature; \(w_{i}\) and \(w_{j}\) are learnable weights; \(\varepsilon=0.0001\) is used to ensure numerical stability. The ECA module, built upon the weighted fusion, employs a local cross-channel interaction strategy without dimensionality reduction. It compresses spatial information through global average pooling and adaptively selects one-dimensional convolution kernel sizes to learn crucial information from different channels, further optimizing the feature fusion process. Its structure is depicted in Figure 9.  
Considering network complexity, the proposed E-BiFPN structure described in this paper includes only one skip connection. Taking the \(P_{4}\) layer as an example, the feature fusion process is illustrated by Equations (3) and (4):  
\[P_{4}^{td}=Conv\Bigg{(}\frac{w_{1}.P_{4}^{in}+w_{2}.Resize(P_{5}^{in})}{w_{1}+ w_{2}+\in}\Bigg{)} \tag{3}\]  
\[P_{4}^{out}=Conv\Bigg{(}\frac{w_{1}^{\prime}.P_{4}^{in}+w_{2}^{\prime}.P_{4}^{ td}+w_{3}^{\prime}.Resize(P_{3}^{out})}{w_{1}^{\prime}+w_{2}^{\prime}+w_{3}^{ \prime}+\in}\Bigg{)} \tag{4}\]  
Figure 8: The E-BiFPN network structure.  
Figure 9: ECA module.  
where \(P_{4}^{in}\) represents the input to feature layer \(n\); \(P_{4}^{out}\) represents the output of feature layer \(n\); \(Conv\) denotes the convolution operation; _Resize_ usually refers to upsampling or downsampling operations. Compared with the previous version, the E-BiFPN structure improves the feature extraction capability for multi-scale engineering-vehicle targets by aggregating image features multiple times, without significantly increasing computational overhead.