# Image-Based Crack Detection Using Total Variation Strain DVC Regularization
## 1 Introduction  
Image-based crack detection is a significant subfield of image analysis that has garnered considerable attention in recent years [1]. Typically, cracks in materials occur at the microscopic level, and their early detection can prevent further damage. When identifying cracks through images, it is crucial to employ methods that effectively preserve the spatial resolution of the analyzed problem, ensuring, at the same time, minimal influence from image noise. However, it is important to note that crack-detection methods based on Digital Volume Correlation (DVC) techniques tend to be insufficient in addressing this aspect. This limitation often presents users with a trade-off, forcing them to choose between a solution that offers higher spatial resolution but lower signal-to-noise ratio (SNR), or vice versa. Visual inspection remains a common method for detecting cracks, yet it is prone to limitations such as subjectivity and reliance on the expertise of the specialist. Moreover, it is time-consuming and exhibits low reproducibility, especially in the case of 3D analysis [2]. As a result, there is a growing need to develop alternative crack-detection methods that are more accurate, efficient, and consistent. Over the years, image-based methods for crack detection have been developed to address the limitations of manual annotation. These methods offer several advantages, including automation, efficiency, and improved reliability. Image-based crack-detection methods can be broadly classified into two categories: direct methods and indirect methods. Direct methods are based on variations in gray scale or color pixel intensities [3], as shown in Figure 1a. Indirect methods rely on the results of Digital Image and Volume Correlation techniques (DIC/DVC), as shown in Figure 1b. Direct methods typically involve a pre-processing step [1; 4; 5], such as smoothing, filtering, or contrast enhancement, followed by a detection step, which may use morphological, statistical [6; 7] (e.g., Gabor filter bank (GFB), Grey Level Co-occurrence Matrix (GLCM), Local Binary Matrix Feature Extraction (LBFE)), or machine learning methods [1; 8; 9]. Pixel-intensity-based crack detectors depend on the lighting conditions and require a homogeneous appearance of the uncracked areas [10]; indeed one of the main limitations of the image-based techniques is that the surface noise might be considered a crack [11]. In DIC, to mitigate this problem, often the cracks are painted in white, but this is not possible for 3D problems. Moreover, pixel-intensity-based methods can achieve a precision more than one order of magnitude below the pixel's size [10] and they are unable to detect the direction of the propagation of cracks properly [11]. To overcome the limitations of direct image-based crack measurements, there has been an increasing use of indirect techniques based on DIC and DVC [10; 12]. However, the main advantage of direct over indirect methods is that they do not require a pre-deformed acquisition (reference frame) and an acquisition in the deformed configuration. The proposed crack-detection method belongs to the category of indirect methods, which rely on information provided by the displacement and/or strain field. In contrast to direct methods, indirect methods identify cracks by detecting discontinuities in the displacement field, which correspond to peaks in the strain field [10; 13]. The displacement and strain fields used in this study are computed from images using digital image and volume correlation techniques [14]. From a mechanical perspective, the use of DVC to compute the strain field can provide valuable insights into the deformation behavior of the material and its response to external loading conditions. The accurate computation and analysis of the strain field is critical in indirect image-based crack-detection methods: modeling a sharp strain field that can describe abrupt deformations is challenging.