###### Abstract  
Crack detection plays a vital role in concrete surface maintenance. Deep-learning-based methods have achieved state-of-the-art results. However, these methods have some drawbacks. Firstly, a single-sized convolutional kernel in crack image segmentation tasks may result in feature information loss for small cracks. Secondly, only using linear interpolation or up-sampling to restore high-resolution features does not restore global information. Thirdly, these models are limited to learning edge features, causing edge feature information loss. Finally, various stains interfere with crack feature extraction. To solve these problems, a pyramid hierarchical convolution module (PHCM) is proposed by us to extract the features of cracks with different sizes. Furthermore, a mixed global attention module (MGAM) was used to fuse global feature information. Furthermore, an edge feature extractor module (EFEM) was designed by us to learn the edge features of cracks. In addition, a supplementary attention module (SAM) was used to resolv interference in stains in crack images. Finally, a pyramid hierarchical-convolution-based U-Net (PHCNet) with MGAM, EFEM, and SAM is proposed. The experimental results show that our PHCNet achieves accuracies of 0.929, 0.823, 0.989, and 0.801 on the Cracktree200, CRACK500, CFD, and OAD_CRACK datasets, respectively, which is higher than that of the traditional convolutional models. convolution neural network; image segmentation; crack detection; U-Net; crack segmentation Article  
With the development of deep learning, image processing techniques based on deep learning have been widely applied in the fields of image classification, object detection, and image segmentation, and have achieved great results. The reason for this is that deep-learning-based methods can automatically extract features from images. Therefore, researchers have begun to apply these methods to concrete crack detection tasks. For example, the FCN [4] model was proposed by [PERSON] for crack detection. In his model, a fully convolutional CNN was used as a crack feature extractor. This structure was able to extract high-level features and encode these features through hierarchical convolution. Then, the encoded features were restored with up-sampling layers. Finally, softmax [5] was used to calculate the category information of each pixel in crack images. However, the edge of the segmentation results generated by the FCN was not very smooth. To solve this problem, [PERSON] [6] proposed using conditional random field (CRF) to improve the results. The CRF method is a graph model that can perform \"smooth\" segmentation based on the pixel intensity of the image. In CRF, points with similar pixel intensities are labeled as the same category. Thus, CRF could make the edge of the segmentation results smoother. Based on the methods proposed above, [PERSON] [7] designed a DeepLab model to process the crack detection task for the purpose of expanding the receptive field of the model. In his design, cascaded expansion convolution was used to expand the receptive field. On the basis of DeepLab, [PERSON] [8] proposed a U-Net model. In U-Net, the feature encoder and decoder adopt a U-shaped symmetry structure, which is effective in the restoration of high-level features. In addition, skip connections were also used in the U-Net model, which can fuse features of the corresponding layers of the feature encoder and the feature decoder. However, extension models based on U-Net above some obvious drawbacks:  
1. Firstly, due to the varying shapes and sizes of cracks, using a single-sized convolutional kernel in crack image segmentation tasks may result in feature information loss for small cracks;
2. Secondly, these models only use linear interpolation and up-sampling operations to restore high-resolution features, and do not restore global information;
3. Thirdly, due to the variable shape of crack features, the accuracy of the model largely depends on the effectiveness of edge feature extraction.