## 2 Materials and Methods
### Point Cloud Coarse Registration Based on Control Points  
The spatial reference and observation viewpoint of TLS and HLS point clouds are so different that it is difficult to strictly establish a point-to-point correspondence, so the point cloud registration algorithm based on a coarse-to-fine strategy is presented. Considering there are repetitive, symmetrical, and incomplete structures in an underground mine, the extraction accuracy of the natural features is low, so the target spheres are laid out and identified to coarsely align the multi-platform point cloud.  
In an underground mine, control points are usually fixed to the rock on the roadway roof using cement nails, and the roadway is surveyed by hanging lines with engineering wires. In our study, for extracting the coordinate information of the control points, the roof control point is introduced to the roadway bottom and the target spheres are placed on the tripod to carry out the centering and leveling operation, and then the center coordinates of the target spheres are calculated according to the diameter of the target and the instrument's height. After collecting the point cloud, considering the target spheres makes it possible to obtain half a spherical point cloud no matter from which direction the laser beam is incident, and the geometric center of the sphere can be obtained by fitting half a spherical point cloud. The mathematical model is:  
\[(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=r^{2} \tag{3}\]  
where \((a,b,c)\) and \(r\) are the center coordinates and the radius of the sphere targets. The fitting process is used to estimate the parameters of the sphere target based on the least squares algorithm using a redundant point cloud.  
The essence of point cloud registration is spatial coordinate transformation, which can be uniquely determined by three types of parameters: scale, rotation, and translation. Considering the scale of the point cloud does not change from before to after registration, only three rotation parameters \(\left(\triangle x\quad\triangle y\quad\triangle z\right)\) and three translation parameters \(\left(\varphi\quad\omega\quad\kappa\right)\) need to be solved, which is called the six-parameter registration model, as shown in Equation (4):  
\[\begin{bmatrix}x_{G}\\ y_{G}\\ z_{G}\end{bmatrix}=R\left(\varphi\quad\omega\quad\kappa\right)\begin{bmatrix}x \\ y\\ z\end{bmatrix}+\begin{bmatrix}\triangle x\\ \triangle y\\ \triangle z\end{bmatrix} \tag{4}\]  
where \(\left(x\quad y\quad z\right)\) and \(\left(x_{G}\quad y_{G}\quad z_{G}\right)\) represent the coordinates of control points from the TLS (or HLS) point cloud and geodetic coordinate system, respectively. After extracting three or more control points' positions, the six-parameter model is adopted to transform the HLS point cloud into the coordinate system where the TLS point cloud is located. However, in an underground mine, there are fewer control point locations where the sphere target can be laid, and the accuracy of the position of the sphere target is low. Therefore, the registration method based on control points can only approximately transform the HLS and TLS point cloud into a geodetic coordinate system.