## 3 Proposed Method
### Attention Gate, Bigger Receptive Field Block  
This layer is integrated into the decoder component of the standard U-Net architecture. By applying the attention mechanism through an attention gate, greater focus is placed on important information via weighting operations at each encoder stage. This is applied along with upsampling to combine the feature maps of the higher levels, ensuring more accurate and detailed segmentation. Figure 4 depicts the attention gate of the proposed network.  
We designed the attention gate as the core module for crack detection in low-resolution images. This module generates weights for attention by passing them through two \(1\times 1\) convolutional layers and a bigger receptive field block (BRFB). The f_prev layer takes the feature from the immediately preceding layer as input. g_skip and f_skip take features from the corresponding layers in the encoder as inputs through skip connections. The difference between the two layers lies in the receptive field sizes of the extracted features. To consider irregular crack features, we minimized the feature loss by bringing features from both small and large receptive fields into the encoder layers and performing summation operations. This allowed us to focus on features that required attention. Within the module, all three layers generate feature maps with coefficient channels, with each coefficient equivalent to the number of channels in the corresponding encoder layer. Details of the larger receptive field block are depicted in Figure 5.  
Figure 4: Details of proposed attention gate.  
Figure 3: Illustration of MSP U-Net.  
Features introduced via the skip connection in the f_skip layer have a limited receptive field compared with those of the previous layer. Like other U-net, we adopted a method using 7 \(\times\) 7, 5 \(\times\) 5, and 3 \(\times\) 3 layers to extract wide context information. This layer recognizes more complex patterns and extracts features from a wider receptive field. By considering the irregularities and varying sizes of cracks, the proposed architecture is capable of learning deeper features. The computed feature maps are summed, followed by the application of the ReLU activation function. The objective functions of the proposed attention gate can be expressed as follows:  
\[f_{prev}(x) =r(W_{x}\cdot x+b) \tag{4}\] \[f_{skip}(y) =r\big{(}W_{y}\cdot y+b\big{)}\] (5) \[g_{skip}(z) =r(W_{z}\cdot z+b)\] (6) \[\alpha =sig\big{(}r\big{(}Wx+Wy+Wz+b_{x,\,y,\,z}\big{)}*(W_{z}+b_{\,z}) \big{)} \tag{7}\]  
where x represents the features of the previous layer, y and z represent features corresponding to the encoder layers with the same values, and \(\alpha\) denotes the attention weight computation result. The ReLU activation function ensures that only positive values remain, whereas negative values are set to 0. After performing a 1 \(\times\) 1 convolution and batch normalization, the sigmoid activation function is applied to obtain the final attention weights. These weights, ranging from 0 to 1, indicate the importance of each pixel. Finally, the attention weights are multiplied by the operation results of the skip connection layer. Our experimental results demonstrate improved edge and detailed crack detection in the decoder layers. Furthermore, the proposed attention block minimizes feature loss, allowing for more accurate target localization. Overall, we successfully achieved multi-feature fusion by combining diverse receptive field features among layers, thereby enhancing crack detection performance.