## 1 Introduction  
The occurrence of cracks is one of the most common damages to a concrete surface and the earliest form of structural failure. The patterns and scales of cracks may reveal the health conditions and damage levels of concrete structures [1]. The widely adopted methods for crack detection include periodic visual inspections, which are inaccurate, expensive, subjective and labor-intensive [2]. Furthermore, because there are many locations on the large structures, such as the bottom of a bridge or spillway of dams, it is often difficult for inspectors to reach the locations, and this renders the monitoring of the cracks for a long period challenging. Over the past decades, many researchers have analyzed the materials using excellent algorithms, have paid attention to numerical simulation schemes to measure the scale and development trend of structural damages [3, 4] or have applied nonlinear analysis to cross-scale modeling to ensure safety [5, 6]. These methods are usually based on existing data for analysis. However, the previously arranged sensors cannot cover new cracks, and it is inconvenient for new contact sensors to be installed on the structural surfaces. Therefore, a non-contact accurate measurement method is needed to measure concrete cracks. With the development of computer vision technology, many crack detection algorithms have been proposed. The traditional crack detection method is the Canny algorithm based on computing digital gradients [7]. However, due to the complex background, the edges of the cracks cannot be uniquely extracted. In recent years, damage identification and concrete structural analysis methods using deep learning with convolutional neural networks (CNN) or artificial intelligence methods have been widely adopted [8]. Deep learning methods have significant advantages compared to traditional image processing techniques or other machine learning techniques [9]. As multilevel features of damages are extracted from the images, deep learning can automatically learn data and update internal parameters continuously to achieve automatic recognition. Deep learning methods have been widely applied for structural health monitoring and are mainly divided into two approaches: object detection and image segmentation based on region division [10]. Considering the patterns of cracks, segmentation methods based on deep learning are suitable for accurately extracting and measuring cracks. The CNN model combined with a sliding window was adopted by [PERSON] to detect cracks on concrete surfaces [9], and the results proved that the deep learning method can extract cracks accurately. To simplify the implementation process and classify the images at the pixel level, an end-to-end architecture based on a fully convolutional neural network (FCN) was conceived [11]. [PERSON] presented the FCN for crack detection, and not only were the cracks reasonably detected but the density was also accurately evaluated [12]. [PERSON] showed the reduced training time of FCN, feeding the train model with 224 \(\times\) 224 size images [13]. Since the image training size can affect the results, the crop size should be carefully considered according to the actual image. There are large numbers of other crack segmentation algorithms based on deep learning that have been proposed [14], and these studies have proven the broad applicability of deep learning. The U-net architecture based on FCN was created by [PERSON] and has become a classical semantic segmentation method [15]. [PERSON] found that the U-net model shows higher accuracy for crack segmentation by examining the fundamental parameters representing the performance of the method, proving that the algorithm can be widely adopted for non-contact measurement [10]. [PERSON] extracted cracks with the combination of CNN classification and U-net segmentation and improved the reliability and efficiency of detecting and differentiating facade cracks from complicated facade noises [16].