# Improved Dab-Deformable Model for Runway Foreign Object Debris Detection in Airport Optical Images
## 3 Methodology
### MDDCA  
In neural networks, the channel attention mechanism [46; 47; 48; 49; 50] is a standard means of feature enhancement. This mechanism explicitly models the channel interdependence, weighs different channel features, and selectively enhances or suppresses features using the learned weights. In this work, we introduce the channel attention mechanism in Deformable DETR and propose our channel attention mechanism, MDDCA, to make the model pay more attention to the more essential features in the image. Figure 4 shows the structure of MDDCA. MDDCA is initially designed to extract channel attention while extracting spatial attention in each channel in different directions. Ultimately, a multi-directional parallel feature extraction is employed. The input feature map is decomposed along the height, width, and channel directions to obtain feature vectors in the three directions. To enhance the network's ability to process spatial information and integrate the spatial data to obtain the attention weight in the direction of height and width, MDDCA uses a deformable convolution, which adaptively adjusts the shape of the convolution kernel according to the offset, along the planar vectors in the directions of height and width. Concurrently, MDDCA computes the channel attention weights of the feature vectors in the channel direction and subsequently fuses the attention weights of these three directions to obtain the multi-directional attention feature map. \[U_{c}=W_{i}*f_{i} \tag{12}\]  
Figure 4: The diagram depicts the MDDCA module’s workflow: (1) three squeeze operations generate feature maps; (2) deformable channel attention enhances the spatial attention features of these maps; (3) scaling operations finally yield multi-scale representations. In this context, \(f_{l}\in R^{(C^{i}\times H\times W)}\) is the input feature map, \(U_{c}\in R^{(C\times H\times W)}\) is the output feature map, and \(W_{i}\in R^{(C^{i}\times C)}\) is a set of \(1\times 1\) convolutional kernels that have been trained to align the features in the input feature vector. \[Z_{h}=\frac{1}{H}\sum_{i}^{H}U_{c}(i,j) \tag{13}\]  
\[Z_{w}=\frac{1}{W}\sum_{j}^{W}U_{c}(i,j) \tag{14}\]  
\[Z_{c}=\frac{1}{H\times W}\sum_{i}^{H}\sum_{j}^{W}U_{c}(i,j) \tag{15}\]  
As demonstrated, statistics \(Z_{h}\) and \(Z_{w}\) are derived from the spatial magnitude of the channels along different dimensions. Global compression yields a statistic \(Z_{c}\) that retains only the information of channel \(U_{c}\). The value of that position on the feature map is \(U_{c}(i,j)\). Subsequently, feature map \(U\) outputs a global statistic vector of size \(H\times W\times C\) via compression. This vector aggregates global information in that direction along different directions of the channel dimension. In addition to the separation of the feature space along the dimensions of \(H\) and \(W\), the feature separation in all three directions is completed by compressing the 2D features into a real number along the channel dimension through pooling. \[S_{h}=\sigma(g(Z_{h},Y))=\sigma(Y_{d2}\delta(BN(Y_{d1}Z_{h}))) \tag{16}\]  
\[S_{w}=\sigma(g(Z_{w},Y))=\sigma(Y_{d2}\delta(BN(Y_{d1}Z_{h}))) \tag{17}\]  
\[S_{c}=\sigma(\varphi(Z_{c},Y))=\sigma(Y_{2}\delta(Y_{1}Z_{c})) \tag{18}\]  
\[F_{l}^{{}^{\prime}}=\frac{1}{3}*(F_{scale}(U_{c},S_{c},S_{h},S_{w}))=\frac{1}{ 3}*[(S_{c}^{U_{c}})\cdot(S_{h}^{U_{c}})\cdot(S_{w}^{U_{c}})] \tag{19}\]  
In this context, \(\delta\) denotes the ReLU activation function, \(\sigma\) denotes the Sigmoid activation function, and \(BN\) denotes the Batch Normalization function. \(g\) is the spatial attention directed toward the input, and \(\varphi\) is the calculation of the channel attention directed toward the input. \(Y_{d1}\in\mathbb{R}^{\hat{\times}C}\) and \(Y_{d2}\in\mathbb{R}^{C\times\frac{1}{\hat{\tau}}}\) are the weight matrices of two deformable convolutional layers. The dimensional decay factor \(r\) is also included in the notation, and \(\frac{c}{r}\) is the number of hidden nodes in the intermediate layer.