## 3 Data Acquisition and Processing
### Multi-Source Point Cloud Fusion  
The ground laser point clouds were highly accurate and fast, but some of them had hollow phenomena. UAV photography measurement was wide and easy to use, while photo-distortion easily occurred in depressed areas, resulting in large data errors and low accuracy, difficult to correct by correction algorithms. In addition, high point cloud accuracy is required for the identification of rock discontinuity surfaces. Therefore, the ground 3D laser point cloud was mainly used, together with the use of the UAV photogrammetry point cloud to compensate for the scanned point cloud voids, to achieve the unity of data integrity and high accuracy. Multi-source point cloud data refer to multiple types of point clouds with different data attributes acquired from multiple sites, multiple time phases, and multiple platforms [17]. Data fusion aims to fuse the data of the same target object according to certain mathematical rules to finally obtain the complete data of the measurement area. In this paper, the ground 3D laser scanning point cloud and UAV tilt photogrammetry point cloud data were processed to achieve multi-point cloud fusion. At present, there are many multi-source point cloud fusion methods, but the common ones are the Iterative closest point (ICP) algorithm [18], the improved ICP algorithm, the unified coordinate system method, etc. Due to the heterogeneity of multi-source data, it is necessary to standardize the multi-point cloud data and unify the data format as \"*.las\" before data fusion. The point cloud data from different data sources have their own coordinate systems; thus, it is necessary to transform and unify them under the same coordinate system. Therefore, we fused the point clouds in two steps: first, to roughly fuse the point clouds through a unified coordinate system; second, to precisely fuse them through the improved ICP algorithm. The unified coordinate system method is based on homonymous points, which can be target spheres or obvious feature points, and it mainly solves the case that the initial positions of data are too far apart. To convert the point cloud data in different coordinate systems to the desired coordinate system, we found more than three sets of homonymous point pairs so that the homonymous point pairs (Pi, Pj) could satisfy the same transformation (\(R\), \(m\), \(T\)). \[\left[ \begin{array}{c}X\\ Y\\ Z\end{array} \right]=mR\left[ \begin{array}{c}x\\ y\\ z\end{array} \right]+T\left[ \begin{array}{c}x0\\ y0\\ z0\end{array} \right] \tag{1}\]  
\[R=\left( \begin{array}{ccc}\cos\alpha&-\sin\alpha&0\\ \sin\alpha&\cos\alpha&0\\ 0&0&1\end{array} \right)\left( \begin{array}{ccc}\cos\beta&0&-\sin\beta\\ 0&1&0\\ \sin\beta&0&\cos\beta\end{array} \right)\left( \begin{array}{ccc}1&0&0\\ 0&\cos\lambda&-\sin\lambda\\ 0&\sin\lambda&\cos\lambda\end{array} \right) \tag{2}\]  
where \(m\) is the scale parameter, \(R\) is the rotation matrix, and \(T\) is the translation matrix, which denotes the rotation angle along the \(X\), \(Y\), and \(Z\) axes. Meanwhile, the coarse alignment accuracy was evaluated by the root-mean-square error (\(RMSE\)) based on the selected homonymous point pairs, which is given by  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(xi-x\hat{x_{i}}\right)^{2}}{n}} \tag{3}\]  
where \(n\) is the number of corresponding point pairs, \(xi\) is the Euclidean distance between homonymous pairs after alignment, and \(x\hat{x_{i}}\) is the true value of the distance between homonymous pairs. Based on the five control marker target points laid out, the exact coordinates were obtained in the point cloud (Figure 8) and corresponded to the GPS acquisition CGCS 2000 coordinate points one by one (Table 2), and the \(RMSE\) = 0.0308554 was calculated according to the fusion effect. The unified coordinate system method transforms different coordinate systems so that the point clouds collected by both 3D laser scanning and UAV photogrammetry are in CGCS 2000 coordinate system.