## 4 Case Study
### Concrete Crack Detection Using the Proposed System  
The practicability of the proposed system was verified by performing crack width measurement on several concrete walls, and the trained model for crack segmentation is the same as the previous model. Compared with the ground truth, the crack area can be extracted from different backgrounds as shown in Figure 23b,d. In addition to the artificial marks wrongly identified as cracks in Figure 23a, blurred boundaries can affect the effect of crack segmentation as Figure 23c. When the background and the cracks are more distinguished, as in Figure 23e,f, the cracks can be better extracted, but the unclear crack in (f) is not completely identified. The boundaries of cracks on concrete structures are usually not clear enough, which cases the edges of U-net segmentation results to be different from the results of the mathematical calculation, and the refinement operation significantly improves the effect of crack extraction. The measurement procedures were carried out under different photographing distances and angles--details are shown in Table 7. The trend of error distribution is similar to the previous verification results, and the maximum error occurs at the furthest position, which is calculated as \(-0.15\) mm measured from \(15.647\) m. For cracks with a small captured angle, the relative error is less than \(5\%\). The proposed system is also applied to a concrete dam to measure the cracks on the concrete pier, as shown in Figure 24. To facilitate verification, the capturing distance and angle are small. Cracks on a concrete dam are usually composed of complex backgrounds, making the segmentation effect different. To analyze the algorithm's ability to extract cracks, the captured images are divided into sizes of \(256\times 256\), and some typical examples are used for analysis as shown in Figure 25. The artificial marks are still misidentified as cracks in Figure 25b,f. The partial recognition effect of crack form changes is affected by the blurry boundaries, as in Figure 25d,g. Furthermore, Figure 26 presents some original captured  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Item** & **Absolute Error** & **Maximum** & \(\mathbf{R^{2}}\) \\  & **Average** & **Absolute Error** & \\ \hline Image 1 & 0.0508 & 0.1290 & 0.9948 \\ Image 2 & 0.0659 & 0.1400 & 0.9960 \\ Image 3 & 0.0578 & 0.1520 & 0.9937 \\ Image 4 & 0.0894 & 0.2750 & 0.9854 \\ Image 5 & 0.0770 & 0.1950  
crack images and the combination of each 256 \(\times\) 256 size image after crack segmentation and Canny processing. With the simple background as shown in Figure 26a,c,e, the crack extraction results are consistent with the actual case, and the misidentified noise and artificial marks are reduced. However, when the concrete surface is uneven or full of holes, as in Figure 26b,d,f, the darker part of the image will be mistaken for a crack. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**Standard (mm)**} & \multicolumn{2}{c}{**Parameters**} & \multicolumn{3}{c}{**Crack Width and Error**} \\ \cline{3-8}  & & **Distance \(U\) (m)** & **Horizontal \(\theta_{h}\)** & **Vertical \(\theta_{v}\)** & **Measured (mm)** & **Error (mm)** & **Relative Value** \\ \hline Crack (a) & 0.77 & 14.851 & 9\({}^{\circ}\) & 2\({}^{\circ}\) & 0.778 & \(-\)0.008 & \(-\)1.04\% \\ Crack (b) & 1.30 & 6.187 & 37\({}^{\circ}\) & 6\({}^{\circ}\) & 1.169 & 0.131 & 10.08\% \\ Crack (c) & 2.74 & 7.348 & 24\({}^{\circ}\) & 10\({}^{\circ}\) & 2.659 & 0.081 & 2.96\% \\ Crack (d) & 3.05 & 15.647 & 25\({}^{\circ}\) & 3\({}^{\circ}\) & 2.900 & 0.150 & 4.92\% \\ Crack (e) & 4.07 & 14.592 & 14\({}^{\circ}\) & 3\({}^{\circ}\) & 3.965 & 0.105 & 2.58\% \\ Crack (f) & 2.11 & 14.851 & 20\({}^{\circ}\) & 1\({}^{\circ}\) & 2.098 & 0.012 & 0.57\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Measurement results of six cracks on concrete wall. Figure 23: Segmentation results of cracks in outfield captured from different positions.