# Concrete Crack Width Measurement Using a Laser Beam and Image Processing Algorithms
## 1 Introduction
[PERSON] et al. [26] attached a transparent scale to the surface of a concrete block being measured and used image processing techniques such as thresholding and sub-pixel interpolation for crack width measurement in millimeters. [PERSON] et al. [6] were able to measure the width of cracks on images in millimeters by utilizing a rangefinder and three laser points projected onto the measured surface, which were used to calculate the corrected angle of the measured plane, \(cos\theta\). [PERSON] et al. [6] then used the corrected angle of the measured plane in Equation (1) to find the ratio of actual width and pixel width (\(J\)). \[J=\frac{(L-f)\cdot d}{f\cdot D}cos\theta\ (\mathrm{mm}/\mathrm{pixel}) \tag{1}\]  
where \(L\) is distance, \(f\) is the focal length, \(d\) is the longest dimension of the image sensor, and \(D\) is the number of pixels along the long side of the image sensor. [PERSON] and [PERSON] [13] measured the maximum crack width using the Euclidean distance transform and the least squares principle. The maximum crack width was measured in millimeters by using the relation between pixel distance and real distance, acquired using a laser range finder, camera field of view, and camera distance to the surface. [PERSON] et al. [19] and [PERSON] and [PERSON] [27] converted the crack widths measured in pixels to millimeters by using the camera pinhole model [28], as shown in Equation (2). \[W_{r}=D_{p}W_{p}=\frac{10\ D_{w}W_{p}}{P_{c}L_{f}} \tag{2}\]  
where \(W_{r}\) is the real crack width in millimeters, \(D_{p}\) is the camera resolution, \(W_{p}\) is the crack width in pixels, \(D_{w}\) is the working distance in mm, \(P_{c}\) is the pixels per centimeter of the camera and \(L_{f}\) is the focal length of the camera in mm. [PERSON] et al. [29] used Otsu image processing to measure crack width in pixels. The crack width was converted to millimeters using a proposed equation shown in Equation (3). \[CW=GSD\times N_{m}=\left(\frac{L-f}{f}\times\frac{S_{S}}{S_{R}}\right)\times N_{m} \tag{3}\]  
where \(CW\) is the crack width in millimeters, \(GSD\) is the ground sample distance, \(N_{m}\) is the number of measured pixels, \(L\) is the working distance, \(f\) is the focal length, \(S_{S}\) is the horizontal dimensions of the sensor, \(S_{R}\) is the horizontal or vertical resolution values in pixels of the sensor. Previous methods for measuring concrete crack width are effective, but they are not without limitations. The need for knowledge of key parameters such as the camera properties such as resolution and focal length has a direct impact on accuracy. The use of incorrect parameters can lead to inaccurate measurements. Other methods face limitations, such as the requirement for markers or scales to be attached to the measured surface. These methods pose significant safety hazards in areas of low accessibility. The aim of this paper is to overcome these limitations by developing a novel concrete crack width measurement method. This is achieved by proposing an affordable and highly flexible approach that utilizes laser beam and image processing algorithms. The crack width is measured in millimeters without the need to know any camera parameters or the need to attach markers or scales to the structure. The effectiveness of this approach is demonstrated through a laboratory experiment and images captured in the real world. The advantages of this method include its ease of application, promotion of safer inspections in hazardous cases, and the ability to measure crack width in millimeters. This method will allow inspectors to interpret results and compare them to allowable limits in international guidelines and codes typically stated in SI or metric units.