## 2 Methodology
### Development of Displacement Extraction Algorithm from Point Clouds  
The first step in non-contact displacement extraction in a concrete experiment is to select labels corresponding to concrete using the Density-based spatial clustering of applications with noise (DBSCAN) algorithm and remove other clusters. DBSCAN is one of the most widely used methods for labeling point clouds and is a non-parametric algorithm that identifies adjacent points within a specified threshold distance as one label. Since DBSCAN forms a non-linear cluster, it can build a cluster for any non-linearity, and it is effective in removing noise by recognizing outliers outside the threshold distance as another cluster [18; 19]. By applying the DBSCAN algorithm, each classified cluster is given a labeling number consisting of a number that gradually increases from one, and then a Region of Interest (ROI) extraction mask is produced by extracting a labeling number corresponding to a concrete coordinate point. The ROI extraction mask designates the concrete area as 1 and other labeled parts (side-attached LVDT sensors, people, background, noise) as 0, and is applied to the raw data of the point cloud to remove unnecessary parts. A flowchart of the applied algorithm is illustrated in Figure 2.  
Despite the expectation that the edge of concrete would be linear, the point clouds extracted from LiDAR exhibit a nonlinear trend due to noise, as shown in Figure 3. To correct the noise in the measurement data, regression analysis was employed [20]. Since RC structures typically have a simply linear structural behavior with respect to rigid body motion, one-dimensional linear fitting was applied to correct the data of the distorted point cloud and derive new left boundary points. The processing of the extraction was repeated for all data measured over the structural loading test.  
\begin{table}
\begin{tabular}{c c} \hline
**Instrument Type** & **Value** \\ \hline Available range of depth distance & 250–9000 mm (only interior) \\ \hline Depth accuracy & 5 mm \\ \hline Depth field of view (FOV) & 70\({}^{\circ}\) (H) \(\times\) 55\({}^{\circ}\) (V) \\ \hline Depth output resolution & 1024 (H) \(\times\) 768 (V) \\ \hline RGB frame resolution & 1280 (H) \(\times\) 720 (V) \\ \hline Maximum measurable speed & 30 Hz \\ \hline \end{tabular}
\end{table}
Table 1: LiDAR equipment specifications.  
Figure 2: An algorithm of displacement extraction from point clouds.  
The collected point cloud data may contain inaccurate points, known as mixed-pixels, due to discontinuities in space at the interface of an object. [PERSON] et al. (2007) and [PERSON] et al. (2009) reported that LiDAR emits a laser with a certain width of diameter to determine distance from the target [21,22]. The diameter of the laser beam is designed to be small, often in the range of a few millimeters to a centimeter. If the laser point reflects off both foreground and background surfaces simultaneously within the diameter of one laser point, the distance measurement will be incorrect. Additionally, micro-angle changes at the edge of the concrete can cause point distortion or omission. Point distortion or noise is problematic for displacement extraction from concrete surfaces; however, increasing the resolution of the point cloud can be a solution. In this study, the resolution of the point cloud in the vertical and horizontal axes was less than 1 mm, as shown in Table 2, which is less than the resolution of LVDT. Therefore, the error rate of the displacement measurement in concrete structures is possibly minimized in this study.