## 5 Results and Discussion
### Comparison with the State-of-the-Art Methods  
In order to evaluate the performance of our proposed PHCNet, we conducted an experiment. We used segmentation accuracy as the main indicator. For the purpose of demonstrating the effectiveness of our proposed model, we used several mainstream crack detection methods as our baseline. Before our comparison, we provide some relevant explanations for these mainstream algorithms:  
FCN [28]: a fully convolutional neural network. ConvNet [29]: a deep convolutional neural network. Split-Attention Network [30]: a channel-wise attention-based network. Cascaded Attention DenseU-Net [31]: an attention-based network with global attention and core attention. ECA-Net [32]: a lightweight-channel attention-based convolutional neural network. DWTA-U-Net [33]: a U-Net based network with discrete wavelet-transformed image features. U-Net proposed by [PERSON] without pretrained model [14]: a U-Net-based network proposed by [PERSON] that was not pretrained with ImageNet. In order to make a fair comparison, the ResNet backbone of this model is not pre-trained by ImageNet. Two-stage-CNN [34]: a two-stage CNN proposed by [PERSON]. As shown in Table 1, compared with the mainstream extended U-Net models, (DWTA-U-Net, ECA-Net, Cascaded Attention DenseU-Net, Split-Attention Network, Alessandro-U-Net without pretrained model, two-stage-CNN), our proposed PCHNet could achieve much better segmentation accuracy on the four public datasets. This strongly proves the effectiveness of our proposed model. Specifically, the Pyramid Hierarchical Convolution Module (PHCM) could extract features of cracks of different sizes since PHCM contains a series of convolution kernels \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Methods** & **Cracktree200** & **CRACK500** & **CFD** & **OAD\_CRACK** \\ \hline CrackForest [35] & 0.08 & 0.199 & 0.104 & 0.08 \\ SVM [36] & 0.382 & 0.418 & 0.32 & 0.215 \\ FCN [28] & 0.39 & 0.513 & 0.585 & 0.416 \\ ConvNet [29] & 0.471 & 0.591 & 0.579 & 0.422 \\ U-Net by [PERSON] [37] & 0.75 & 0.681 & 0.851 & 0.681 \\ U-Net by [PERSON] [38] & 0.763 & 0.695 & 0.856 & 0.683 \\ Split-Attention Network [30] & 0.851 & 0.73 & 0.963 & 0.696 \\ Cascaded Attention & 0.863 & 0.74 & 0.97 & 0.695 \\ DenseU-Net [31] & 0.885 & 0.753 & 0.971 & 0.711 \\ DWTA-U-Net [35] & 0.90 & 0.77 & 0.973 & 0.729 \\ U-Net proposed by Di & & & & \\ without pretrained model [14] & 0.791 & 0.732 & 0.887 & 0.715 \\ Two-stage-CNN [34] & 0.892 & 0.79 & 0.981 & 0.735 \\ PHCNet & 0.929 & 0.823 & 0.989 & 0.801 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with the state-of-the-art methods. with different sizes. Thus, the features extracted by PHCM could adapt varying shapes and sizes of cracks. Also, PHCM can extract multi-scale crack information without increasing the number of parameters and model complexity. Additionally, the Mix Global Attention Module (MGAM) is used to fuse global feature information, guiding the model in the restoration of high-resolution features with global information. Furthermore, the Edge Feature Extractor Module (EFEM) could learn the edge features of cracks by adding edge-detection operators Sobel, Laplacian, and Canny. Since these operators could provide a multi-view of edge features in our model. In addition, the Supplementary Attention Module (SAM) could solve the interference caused by stains in crack images, since it could continuously remove the crack features that have already been extracted by the model from the high-level output to compel the model to learn new crack features, allowing for the model to automatically and continuously learn supplementary detailed features. Compared with the U-Net model, attention-based models such as ECA-Net, Cascaded Attention DenseU-Net, Split-Attention Network, DWTA-U-Net could achieve a better performance, since these models use attention block to decrease the interference caused by shadow and light.