## 4 Discussion  
In this study, a methodology was proposed for the localization of concrete cracks using unmanned aerial vehicle-based aerial images when there is a lack of reference objects and feature points within the images. The use of unmanned aerial vehicles for image-based safety inspections allows data to be obtained from hard-to-reach areas. It minimizes the subjective intervention of inspectors, ensuring the objectivity of the investigation results. Moreover, it improves constraints on the timing and location of inspections, leading to reduced manpower and cost for conventional inspections and surveys. Due to these advantages, research utilizing unmanned aerial vehicles for safety inspections, including buildings and other facilities, has been actively conducted in recent times. However, current studies related to safety inspection, such as the study of [PERSON] et al. [9], focus only on the detection of cracks. Although there were previous studies related to the location of cracks, the studies also focused on the detection and identification of cracks and the location of cracks was roughly expressed [43; 44; 45; 46; 47]. In addition, [PERSON] et al. [23] conducted a study on the localization of cracks using an image processing technique using a reference object, but when the facility to estimate the location of the crack does not have a feature point that can be defined as a reference object, there was a limitation that the methodology could not be used. The methodology proposed in this study overcomes these limitations, and using experimentation and validation, it has been confirmed that crack localization is possible even when reference objects and feature points are lacking. In this study, the localization of cracks was estimated by applying an unmanned aerial vehicle and image processing techniques, which have recently attracted attention in safety inspection. Compared to previous studies, this study is differentiated in that it provides a methodology that can localization of cracks even when reference objects in the target building are insufficient or do not exist. In addition, it is expected that the utilization of unmanned aerial vehicles during safety inspection can be increased in that the technology that has been attracting attention has been applied. However, this study has a limitation in that it designed a separate Laser Point model to be attached to the unmanned aerial vehicle for the supplementation of reference objects and feature points. Many researchers have conducted studies using unmanned aerial vehicles and deep learning to detect cracks. It is anticipated that the fusion of this study with crack detection technology in the future could make a significant contribution to safety inspections. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Classification**} & \multicolumn{2}{c}{**Ground Truth Values (\(\Delta\)x, \(\Delta\)y), (Unit: mm)**} \\ \hline Crack 1 & (1032, 21) \\ Crack 2 & (30, \(-1699\)) \\ Crack 3 & (\(-238,-1212\)) \\ Crack 4 & (\(-609,49\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of measured ground truth distance to cracks (Location from start point to end points of cracks). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & \multicolumn{4}{c}{**Relative Position (\(\Delta\)x, \(\Delta\)y), (Unit: mm)**} \\ \cline{2-5}  & **Coordinate** & **Ground Truth** & **Estimate** & **Error** & **RMSE** \\ \hline \multirow{2}{*}{Crack 1} & x & \(1211\) & \(1098\) & \(111\) & \(80.80\) \\  & y & \(40\) & \(23\) & \(-7\) & \\ \hline \multirow{2}{*}{Crack 2} & x & \(-20\) & \(-32\) & \(-12\) & \\  & y & \(-1721\) & \(-1868\) & \(-113\) & \\ \hline \multirow{2}{*}{Crack 3} & x & \(231\) & \(254\) & \(23\) & \\  & y & \(-1474\) & \(-1332\) & \(-119\) & \\ \hline \multirow{2}{*}{Crack 4} & x & \(494\) & \(648\) & \(94\) & \\  & y & \(49\) & \(54\) & \(10\) & \(108.95\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of estimated relative positions and measured relative position values.