## 4 Construction of Octree-Based Shape Information Model
### Image Processing for Crack Detection
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**True Positive**} & **False Negative** & \multirow{2}{*}{**Number of False Positive**} \\ \cline{1-1} \cline{3-4} Original & 100\% (19/19) & 0\% (0/19) & 0 \\ Case 1 & 95\% (18/19) & 5\% (1/19) & 10 \\ Case 2 & 84\% (16/19) & 16\% (3/19) & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantitative comparison of the three cases. Figure 13: The image results by the proposed method for three cases. (**a**) Crack map by visual inspection; (**b**) Original image; (**c**) Case 1; (d) Case 2. For comparative evaluation, [PERSON]'s method [51] was applied to the original image as well. [PERSON]'s method was developed to detect cracks in photographic images, and it has the following summarized steps. 1. Convert RGB image to grayscale. 2. Use the Sobel edge detector to find the edges with masks and get the value of the edge image. 3. Use [PERSON]'s thresholding value to obtain the binary image. 4. Find the connected areas in the binary image with the controlled area and put them to the background. First, [PERSON]'s method for a clear crack case with some stains was applied and compared with the proposed one, as presented in Figure 15. The results in Figure 15 show that [PERSON]'s method detected some undesirable areas such as stains, making it difficult to distinguish them from the major and minor cracks on the concrete surface. Figure 14: The cracks identified by the proposed method for three cases. (**a**) Crack map by visual inspection; (**b**) Original image; (**c**) Case 1; (d) Case 2. Figure 15: The comparison of the proposed method with [PERSON]’s method for a clear crack case. (**a**) Clear crack case; (**b**) [PERSON]’s method; (**c**) Proposed method. Moreover, the filtering by the classification in the proposed method was more effective in our case which had more stains, sediments, and joints, as shown in Figure 16. Thus, the proposed method outperforms in detecting cracks with the help of properly selected image processing algorithms. The K-means clustering significantly helped to remove many parts related to structural joints and sediments while keeping crack objects. Based on the other image processing algorithms, such as improved subtraction and morphological operations, the crack objects were comparably identified while minimizing the noises. Though the quantitative accuracy was not achieved due to the difficulty in assessing the target structure in detail, the visual comparison of Figure 16b,c clarifies the effectiveness of the proposed method in detecting the cracks even by the scanning 30 m distant from the test structure. After detecting the cracks using the proposed method, quantification of cracks can be done by employing existing quantification algorithms mostly based on combination of morphological operations, such as median filtering, morphological opening and closing, skeletonization, edge detection, etc. [52; 53; 54; 55]. Though the lengths and widths of cracks are not quantified in this study, the crack widths obtained by visual inspection in Figure 16a are within 0.2 mm. According to the Korean structural inspection guide, a crack width less than 0.1 mm leads to the grade of the inspected structure as \"a\", and width between 0.1 mm and 0.3 mm leads to \"b\" [56]. Thus, the proposed method can be successfully used as a prospective alternative to the conventional visual inspection of large structures with minimal labor and logistics time.