# Region-Based CNN Method with Deformable Modules for Visually Classifying Concrete Cracks
## 1 Introduction  
In the field of structural condition assessment, cracks are usually the most intuitive and relatively reliable indicator for evaluating the performance of a structure [1]. Based on audiovisual methods, stress-wave methods, and electromagnetic methods, plenty of research on the detection of structural cracks has been carried out [2; 3]. Currently, the main methods can be divided into two categories: one type based on acoustic waves [4] and the other type based on image analysis [5]. As early as the 1990s, the acoustic emission (AE) technology was gradually promoted and used to test the integrity of concrete structures in Japan, although it was not always successful when applied to practical problems. With the development of testing equipment, [PERSON] and [PERSON] [6] classified crack patterns in concrete by the AE technology. On this basis, [PERSON] [7] conducted an experiment to monitor several types of concrete crack during bending, and further proposed and clarified some AE indicators that can classify the crack mode under different stress states. [PERSON] et al. [8] proposed a new probabilistic method based on the AE Gaussian mixture model (GMM) that can more efficiently classify the crack patterns in reinforced concrete structures. [PERSON] and [PERSON] [9] also adopted the AE signals to classify crack types of reinforced concrete beams subjected to four-point bending. Over the past years, portable AE equipment has been applied to monitor the cracks in prefabricatedprestressed concrete beams during construction [10]. As an effective method for classification of structural cracks, the AE method has high demand on equipment and is seriously affected by noise. Unlike the AE method, the image analysis method uses images of the structure surface to identify structural cracks. During the past decades, traditional vision inspection has been developed from naked-eye inspection to the machine-vision inspection. Currently, naked-eye inspection is still the most common method used to identify structural cracks. However, this method is often time-consuming and subjective, and can be dangerous in some circumstances. To tackle these issues, many studies have been conducted on automatic detection of cracks based on the machine vision technology. In these researches, many image-processing algorithms, including mathematical morphology [11], digital image correlation (DIC) [12; 13], image binarization [14], percolation model [15], wavelet transforms [16], and edge detectors [17] have been developed to detect cracks in obtained images. Combined with drone technology in civil engineering, the detection of cracks has become more convenient and safer [18; 19; 20]. However, the performance of these methods is susceptible to environmental conditions such as the light conditions. Among the above methods, DIC technology, as a relatively new nondestructive and noncontact full field displacement measuring technique, has been widely applied to the study of concrete fracture [21]. The classical DIC method classifies cracks by comparing the pixel features of the point of interest at different states to those at the initial state [21; 22], which is less affected by environmental noise. However, compared with the intelligent detection method, it still needs to judge the position of the crack artificially before the detection, and its effectiveness is limited by the uncertainty of the constitutive parameters and boundary conditions [23]. In the early 1990s, neural networks were widely applied to crack detection, and one of the most popular multilayer neural networks has been the convolutional neural network (CNN), which is able to recognize crack patterns from images with minimal preprocessing. During the past decade, with the improvement of computing power of high-performance graphics processing unit (GPU), the performance of the CNN has been improved significantly. [PERSON] et al.