## 3 Materials and Methods
### Residual Multi-Scaled Dilated Convolution Branch  
The residual multi-scaled dilated convolution branch employed the dilated convolution pyramid with attention (DCPA) module to capture localized road features effectively. The DCPA module comprised four parallel dilated convolution blocks (PDCB), a global average pooling layer, a channel attention block, and a spatial attention block. Due to the sparsity of HR remote sensing images, incorporating pyramid features without reducing resolution can enhance the model's ability to identify objects and improve overall performance.  
The DCPA module, inspired by [11; 33], is detailed in Table 1 and visualized in Figure 2. The module comprised the parallel dilated convolution blocks (PDCB), which consisted of multi-scale parallel convolution layers with different dilation rates, along with a global pooling layer. The dilated rates used in four parallel paths were 1, 6, 12, 18, respectively, aiming to capture pyramid features and context information of road pixels. The output of the parallel paths was then concatenated and processed by a \(1\times 1\) convolution layer to produce the final output. The dilated convolution layers control the size of the effective receptive field of the convoluted kernels and dilated rate. A larger dilated rate corresponds to a larger scale without reducing feature resolution. Furthermore, the global pooling layer, which operates at the image level, averaged the feature maps across the spatial dimensions to improve the model's ability to recognize global context and capture long-range dependencies. Furthermore, each path in the DCPA module consisted of a convolution layer with a specific dilated rate, followed by the operations of batch normalization (BN) and activation (ReLU).  
The spatial attention component learned to selectively emphasize informative spatial locations by computing an SA map. The map was computed by applying a convolution layer with a 7 \(\times\) 7 kernel and a stride set at 1, followed by a ReLU layer and another convolution layer with a 1 \(\times\) 1 kernel size and a stride of 1. The resulting spatial attention output was then multiplied with the refined feature maps obtained from the channel attention component. The final output of the DCPA module was acquired by concatenating the refined feature maps with the spatial attention map. The DCPA modules are expressed as follows:  
Dilated convolution blocks:  
\[f_{DCP}(X)=\sum_{path}conv(X,dilated\_rate_{path}) \tag{2}\]  
Channel attention blocks:  
\[f_{channel}(X)=\sigma(MLP(AvePool(X)))\times X \tag{3}\]  
where \(X\) is the input tensor, AvgPool represents the global average pooling operation, MLP is a two-layer fully connected network with ReLU activation layers correspondingly, and \(\sigma\) utilizes the sigmoid function.  
Spatial attention blocks:  
\[f_{spatial}(X)=\sigma(conv_{1}(\text{ReLU}(conv_{2}(X))))\times X \tag{4}\]  
where conv1 and conv2 are convolutional layers with kernel sizes of 7 \(\times\) 7 and 1 \(\times\) 1, respectively, and \(\sigma\) is also the Sigmoid layer. The final output of the DCPA module is obtained by merging the refined feature maps with the SA map:  
\[f_{DCPA}(X)=f_{channel}(f_{spatial}(f_{DCP}(X))) \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Items** & **Layer** & **Kernel Size** & **Dilated Rate** \\ \hline PDCB-1 & ReLU(BN(Conv)) & 1 \(\times\) 1 & 1 \\ PDCB-2 & ReLU(BN(Conv)) & 3 \(\times\) 3 & 6 \\ PDCB-3 & ReLU(BN(Conv)) & 3 \(\times\) 3 & 12 \\ PDCB-4 & ReLU(BN(Conv)) & 3 \(\times\) 3 & 18 \\ AvgPooling & ReLU(BN(Conv)) & 1 \(\times\) 1 & - \\ CA & Pooling-MLP-ReLU & - & - \\ SA & Pooling-Conv & 7 \(\times\) 7 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: The settings of the PDSA module.  
Figure 2: The structure of the DCPA module.