# Automated Pixel-Level Deep Crack Segmentation on Historical Surfaces Using U-Net Models
## 2 State-of-the-Art Studies for Crack Segmentation  
This section reviews the most relevant literature addressing pixel-level crack detection techniques. In [11], [PERSON] et al. proposed automatic crack classification and segmentation methods based on a Convolutional Neural Network (CNN) and transfer learning schema for masonry surfaces. The performance of different pre-trained deep learning models was investigated for the crack detection task. Then, both Feature Pyramid Networks (FPN) and U-Net with the best model as the encoder were used for pixel-level crack detection. Meanwhile, in [7], [PERSON] et al. proposed an end-to-end pixel-wise crack segmentation method based on a deep hierarchical CNN having the power of learning and effectively aggregating multi-scale and multi-level features from the lower convolutional layers to the higher ones. Moreover, a loss function was especially designed to alleviate the problem of imbalanced data distribution. Another pixel-level, end-to-end, trainable deep CNN for road crack detection, able to handle strong non-uniformity, complex topology, and strong noise-like problems in the crack images, was proposed in [12] by [PERSON] et al., using a multi-scale dilated convolution module to obtain more abundant crack texture information. Furthermore, [PERSON] in [13] proposed an end-to-end deep fully convolutional network (FCN)-based crack detection method for semantic segmentation on concrete crack images. Moreover, in [14], [PERSON] et al. presented a novel crack segmentation method based on a context-aware deep convolutional network to segment cracks effectively in structural infrastructure under different conditions. Meanwhile, in [15], [PERSON] et al. proposed a hybrid crack detection, localization, and measurement method based on a Faster R-CNN, a modified Tubularity Flow Field (TuFF) algorithm, and a modified Distance Transform Method (DTM) for pixel-level crack segmentation. From another perspective, [PERSON] et al. in [16] proposed a U-Net-based crack image segmentation network for pavement cracks with a one-cycle training schedule for speeding up the convergence. The proposed segmentation network replaced the encoder part of the U-Net neural network with a pre-trained ResNet-34 neural network. [PERSON] et al. in [17] proposed a framework for landslide detection that integrated the ResU-Net deep learning model with rule-based object-based image analysis (OBIA) to improve the detection rate of the ResU-Net model. Based on evaluating the performance of the proposed integrative framework, using the Sentinel-2 imagery dataset, the F1 score value was enhanced by 8% and 22% against the F1 score values achieved by the ResU-Net and OBIA approaches, respectively. In [18], [PERSON] et al. proposed an integrated pixel-level crack detection and quantification approach based on DeepLabv3+ to automatically detect and quantify cracks in asphalt pavement images for operation and maintenance. In addition, they used adjustment of the weight of the different classes to address the problem of class imbalance, skeletonizing, and fast parallel thinning (FPT) techniques for measuring the length, width, area, and ratio of cracks. In [10], [PERSON] et al. presented an encoder-decoder model based on a modified SegNet architecture, which handled arbitrary-sized images for pixel-level crack detection in concrete pavement, a bridge deck, and asphalt pavement, aiming at improving the performance by merging the features of low-resolution input samples. [PERSON] et al. in [19] proposed a pixel-level crack detection method based on Deep Local Pattern Predictor (DLPP) for concrete bridge images, aiming at handling the limitations resulting from noise and clutter in the environment. Finally, in [20], [PERSON] et al. proposed an open-source crack detection platform based on an improved VGG-16 transfer learning model. The proposed platform in this study was capable of detecting multi-scale concrete structure cracks.