## 4 Case Study
### Crack Measurement Tests in Lab
Each crack is measured three times, and the average values are used for analysis; the results are presented in Table 4. Similar to the aforementioned systematic error analysis experiments, larger errors also occur at positions with larger capturing angles, and the errors are minimal when photographed vertically. The average error in each position is 0.066 mm, 0.079 mm, 0.046 mm, 0.078 mm and 0.072 mm, respectively, and the maximum error does not exceed 0.2 mm, which satisfies the accuracy requirements of practical application. To verify the accuracy of the image-measured methods proposed in this study and the effect of capturing angle and distance on measurement results, 12 natural cracks on a concrete wall are selected as a test sample, as shown in Figure 19. As the standard widths of the cracks are measured by an instrument, as shown in Figure 11, 20 images of the concrete wall acquired in different positions have been chosen to compare the widths with standard values; the specific photographing distances and angles are shown in Figure 20. Due to the size of the experimental site, the captured distances \(L\) and horizontal angle \(\theta_{h}\) change from 5 to 20 m and \(-65^{\circ}\) to \(50^{\circ}\), and there is a red laser point on each image, representing the set measurement center points. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{5}{c}{**Average Measurement Results (mm)**} & \multicolumn{5}{c}{**Performance Criteria**} \\ \hline \multicolumn{1}{c}{**Distance**} & \multicolumn{1}{c}{**Horizontal**} & \multicolumn{1}{c}{**Vertical**} & \multirow{2}{*}{**1\# (7.20)**} & \multirow{2}{*}{**2\# (4.20)**} & \multirow{2}{*}{**3\# (2.30)**} & \multirow{2}{*}{**4\# (1.250)**} & \multirow{2}{*}{**5\# (0.70)**} & \multicolumn{1}{c}{**Average**} & \multicolumn{1}{c}{**Maximum Error**} \\ \cline{1-1} \cline{6-11} \(U\) (m) & \(\theta_{h}\) & & & & & & & & **Error** & **Error** \\ \hline
9.776 & \(15^{\circ}\) & \(-3^{\circ}\) & 7.337 & 4.158 & 2.389 & 1.31 & 0.784 & 0.066 & 0.137 \\
15.866 & \(7^{\circ}\) & \(2^{\circ}\) & 7.224 & 4.299 & 2.401 & 1.345 & 0.777 & 0.079 & 0.101 \\
20.369 & \(1^{\circ}\) & \(2^{\circ}\) & 7.209 & 4.267 & 2.326 & 1.299 & 0.78 & 0.046 & 0.08 \\
10.490 & \(-11^{\circ}\) & \(-1^{\circ}\) & 7.327 & 4.303 & 2.276 & 1.378 & 0.756 & 0.078 & 0.128 \\
10.876 & \(-19^{\circ}\) & \(1^{\circ}\) & 7.348 & 4.028 & 2.41 & 1.41 & 0.816 & 0.072 & \(-0.172\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurements results of five artificial cracks. Figure 18: Five artificial cracks: (**a**) original image with measured width; (**b**) segmentation results of the proposed method. Figure 19: Concrete wall with 12 naturally occurring cracks. by Canny algorithm can improve the crack width measurement accuracy. Of these, crack no. 8 is not refined due to the good performance of U-net segmentation. The larger error values occur in images 7 and 20, which are captured at larger horizontal angles. As the larger photographing distance and angle cause the unit pixel size \(\varepsilon\) to be larger, the errors caused by other parameters in Formulas (25) and (29) would be magnified, and larger errors in measurement may result. To confirm the measurement accuracy of the proposed system, the results of the width of each crack in each image are shown in Figure 22. Except for the areas not captured in the images, most of the cracks were detected and gave accurate results. Crack no. 1 and crack no. 7 are not detected in some images, because the narrow crack width resulted in a small number of captured pixels; for instance, the width of crack no. 1 only contains 1 pixel during photographing at a larger side angle, and the shallow depth of field of the camera causes a blur at the edge of the target plane, which makes the narrow crack unrecognizable. Figure 21: Examples of crack segmentation on concrete wall; the blue circle is the location of crack width measurement.