# Swin-YOLO for Concealed Object Detection in Millimeter Wave Images
## 3 Theoretical Model
### The Proposed Object Detection Network
#### 3.2.2 Coordinate Attention Module  
The Coordinate Attention (CA) Module [46] is a lightweight attention module that embeds the object positional information in the channel attention. It can generate attention feature maps in two coordinate directions and resize the weights of the two-dimensional feature maps. By multiplying the input feature map with the attention feature, the final attention feature is obtained, as shown in Figure 3.  
The feature map of the input image is represented as \(F\). The CA module first performs average pooling operations along the horizontal and vertical coordinates of each channel of the input feature vector, obtaining a pair of direction-sensitive feature maps \(z^{h}\) and \(z^{w}\). These two 1D feature encoding processes allow the model to capture long-range dependencies between channels in one direction while preserving the object's positional information in the other direction.  
The intermediate feature map encodes the spatial feature maps along the horizontal and vertical directions. We first concatenate the \(z^{h}\) and \(z^{w}\) feature maps along the spatial dimension and encode them using a shared \(1\times 1\) convolutional function \(F_{1}\), followed by a nonlinear activation function \(\delta\) to output the intermediate feature map \(f\). This is shown in Equation (1):  
\[f=\delta\Big{(}F_{1}\Big{(}\Big{[}\Big{(}z^{h}\Big{)}+(z^{w})\Big{]}\Big{)} \Big{)}, \tag{1}\]  
Then, we split \(f\) along the spatial dimension and use \(1\times 1\) convolutional functions \(F_{h}\) and \(F_{w}\) along different spatial directions to transform the channel numbers of \(f^{h}\) and \(f^{w}\). We then obtain attention weights \(g^{h}\) and \(g^{w}\) with the same number of channels as the input \(F\), as shown in Equation (2):  
\[g^{(h,w)}=\sigma\Big{(}F_{(h,w)}\Big{(}f^{(h,w)}\Big{)}\Big{)}, \tag{2}\]  
where \((h,w)\) represents either \(h\) or \(w\), and \(\sigma\) represents the sigmoid activation function.  
Finally, \(g^{h}\) and \(g^{w}\) are applied to the input feature \(F\) to obtain the final CA feature map \(M_{c}\), as shown in Equation (3):  
\[M_{c}=\ F_{i}\times g^{h}\times g^{w}, \tag{3}\]  
For MMW human body images, the features of the concealed object are similar to those of the human body region. The concealed objects are small with complex textures, which can cause confusion between the detected object and the background, making it difficult to accurately identify the concealed object. Therefore, it is especially important to focus on the key areas of the feature map. After extracting the concealed object features with the backbone network, the multi-scale features are further processed by the neck network. As the key to feature fusion, the neck network can utilize the feature map better.  
Figure 3: The architecture of Coordinate Attention. The Coordinate Attention sub-channel generates attention simultaneously in both X and Y directions. X Avg Pool and Y Avg Pool represent 1D horizontal global pooling and 1D vertical global pooling, respectively.  
Thus, in order to refine the position information in the neck network and fuse the more important information from different depth feature maps, we combine the lightweight Coordinate Attention Module with the neck network of Swin-YOLO to improve the detection performance of the detection head.