## 4 Case Study
### Crack Measurement Tests in Lab  
To comprehensively evaluate the errors of the system and analyze the influence of errors caused by equipment, algorithms and environmental factors, several experiments are carried out step by step. The accuracy verification of the proposed system is mainly divided into the following steps: firstly, the proposed combination of the camera and laser rangefinder is used to measure the size of the grid on the calibration board from different distances to evaluate the systematic error; secondly, standard cracks are artificially generated and segmented by the proposed combination of the improved U-net segmentation algorithm and Canny method to analyze the practicality of the algorithm; finally, the system is applied to the actual cracks on the concrete wall in the laboratory, outfield and concrete dam. The calibration board Is the same as presented previously with a 1 cm grid size and is measured from 9 m to 30 m. Some measurement scenarios are shown in Figure 17, and the results are presented in Table 3. Since there are many grids on the calibration board, the average value of the measurements is used for comparison. The maximum error occurs at the position with the largest horizontal angle, which is \(-\)0.216 mm, and other large errors also occur at larger distances or angles. Meanwhile, it can be seen that the influence of angle on the measurement results is greater than that of distance. The reason for this tendency is that a larger measuring distance or bias angle will reduce the number of pixels that the target occupies in the image, resulting in a larger effect of image resolution and unit pixel size on the target size. Since the corner point extraction algorithm of the calibration board is relatively mature and accurate, the experimental error basically represents the systematic error of the measurement equipment. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Dataset** & **Precision** & **Recall** & **F1** \\ \hline Training & 0.9160 & 0.9224 & 0.9181 \\ Validation & 0.9152 & 0.9171 & 0.9147 \\ Testing & 0.9016 & 0.9164 & 0.9075 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of U-net model for concrete crack segmentation. Figure 17: Some grid size measuring scenarios: the distance, horizontal and vertical angle are (a) 20.2 m, 9\({}^{\circ}\), 4\({}^{\circ}\); (b) 8.7 m, 5\({}^{\circ}\), 1\({}^{\circ}\); (c) 15.4 m, \(-\)31\({}^{\circ}\), \(-\)1\({}^{\circ}\); (d) 18.2 m, 7\({}^{\circ}\). \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{2}{l}{**Parameters**} & \multicolumn{4}{c}{**Grid Size and Error**} \\ \cline{2-5}  & **Distance** & **U (m)** & **Horizontal** & \(\theta_{\text{v}}\) & **Vertical** & \(\theta_{\text{v}}\) & **Average Measured (mm)** & **Error (mm)** \\ \hline
1 & 20.226 & 9\({}^{\circ}\) & 4\({}^{\circ}\) & 10.078 & 0.078 \\
2 & 8.744 & 5\({}^{\circ}\) & 1\({}^{\circ}\) & 10.083 & 0.083 \\
3 & 15.498 & \(-\)31\({}^{\circ}\) & \(-\)1\({}^{\circ}\) & 9.784 & \(-\)0.216 \\
4 & 18.226 & 7\({}^{\circ}\) & 4\({}^{\circ}\) & 10.076 & 0.076 \\
5 & 19.167 & \(-\)13\({}^{\circ}\) & 6\({}^{\circ}\) & 10.118 & 0.118 \\
6 & 30.114 & 10\({}^{\circ}\) & \(-\)3\({}^{\circ}\) & 9.817 & \(-\)0.183 \\
7 & 22.681 & 22\({}^{\circ}\) & \(-\)4\({}^{\circ}\) & 10.200 & 0.200 \\
8 & 25.782 & 8\({}^{\circ}\) & 2\({}^{\circ}\) & 10.158 & 0.158 \\
9 & 14.467 & \(-\)15\({}^{\circ}\) & 5\({}^{\circ}\) & 10.109 & 0.109 \\
10 & 9.265 & \(-\)6\({}^{\circ}\) & 19\({}^{\circ}\) & 10.191 & 0.191 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurements on the grid size of the calibration board. Moreover, five artificial cracks with standard width of 7.2 mm, 4.2 mm, 2.3 mm, 1.25 mm and 0.7 mm are placed on the plane as shown in Figure 18, and the widths are measured by the crack width measuring instrument.