# Analysis of Fine Crack Images Using Image Processing Technique and High-Resolution Camera
## 4 Measurement Results and Analysis
### Analysis of the Causes of Crack Measurement Errors  
Previous researchers pointed out that the causes of errors in crack measurement are in the resolution, image processing method, thresholding process during image processing, and mixed-pixel phenomenon, in which the background is recognized as a crack or a crack is recognized as a background [30]. Nevertheless, based on the results obtained in this experiment, it is judged that the errors occur due to the resolution of the imaging equipment and the range of the applied focal length. Given the basic image processing theory, the smallest unit of digital images is expressed as integers in pixel units [31]. However, in order to accurately measure crack widths, the measured pixel values should be in decimal units, but this is not the case in practice. To help understanding, the measured pixel counts and width values of SC100-0.5 and SC50-0.5 within the same shooting section range among the resulting values derived using SC equipment are shown in Figure 15, where Pm is a pixel value measured through image processing and Pr is a value obtained by dividing the ground truth value by the \(GSD\) value according to the working distance applied to each focal length, which can be calculated using Equation (6). \[Number\ of\ real\ pixels=\frac{Ground\ truth}{GSD} \tag{6}\]  
\[GSD=\frac{L-f}{f}\times\frac{s_{S}}{s_{R}} \tag{7}\]  
\(Wm\) is an area value in consideration of the \(GSD\) value for the number of pixels acquired through image processing. The ground truth is the width value of the virtual image, and it is the area value considering the \(GSD\) value for the actual pixel value. In addition, for ease of reading the figure, only the inflection point parts were expressed using markers. In Figure 15a, it can be seen that PWL-10 values are more precisely measured in the case of SC100-0.5 than SC50-0.5 when the width is measured. Moreover, the position where the measured pixel value and the theoretical actual pixel value intersect was found to be a point with 0% error, as shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & \multicolumn{5}{c}{**PWL-10**} & \multicolumn{2}{c}{**Unit: \%**} \\ \cline{2-7}  & \multicolumn{3}{c}{**SC100**} & \multicolumn{3}{c}{**SC135**} \\ \cline{2-7}  & **0.1 mm** & **0.3 mm** & **0.5 mm** & **0.1 mm** & **0.3 mm** & **0.5 mm** \\ \hline \multirow{5}{*}{\begin{tabular}{c} Working \\ distance \\ (m) \\ \end{tabular} } & 1.00 & 85.18 & 100 & 100 & 95.56 & 100 & 100 \\ \cline{1-1} \cline{2-7}  & 1.50 & 71.15 & 100 & 100 & 82.10 & 100 & 100 \\ \cline{1-1} \cline{2-7}  & 2.00 & \begin{tabular}{c} 51.29 \\ (46.49) * \\ \end{tabular} & 97.40 & 89.44 & 72.41 & 100 & 100 \\ \cline{1-1} \cline{2-7}  & 3.00 & & 90.55 & 100 & \begin{tabular}{c} 46.53 \\ (47.94) * \\ \end{tabular} & 97.95 & 100 \\ \cline{1-1} \cline{2-7}  & 4.00 & & 74.57 & 90.39 & 91.01 & 100 \\ \cline{1-1} \cline{2-7}  & 4.50 & 76.48 & 90.34 & 80.75 & 97.97 \\ \cline{1-1} \cline{2-7}  & 5.00 & 68.06 & 90.08 & 73.03 & 98.20 \\ \cline{1-1} \cline{2-7}  & 5.50 & 61.30 & 81.15 & 75.75 & 89.49 \\ \cline{1-1} \cline{2-7}  & 6.00 & 55.77 & 73.82 & 77.98 & 90.45 \\ \cline{1-1} \cline{2-7}  & 6.50 & \begin{tabular}{c} 51.15 \\ (51.45) * \\ \end{tabular} & \begin{tabular}{c} 75.33 \\ (52.41) * \\ \end{tabular} & \
\begin{tabular}{c} 71.59 \\ (51.94) * \\ \end{tabular} &
\begin{tabular}{c} 91.26 \\ (52.70) * \\ \end{tabular} \\ \hline \hline \end{tabular} ()* Value of PWL-10 at the measurement limit distance.  
\end{table} 
Table 6: Value of PWL-10 within working distance by focal length difference. Given the measurement results shown in Table 8, when a focal length of 50 mm is applied at a 400 mm point, the pixel value should be 18.85 to become a value of 0.5 mm width, but in reality, the pixel value measured through image processing was 19.