## 3 Improved Point Cloud Comparison Method  
### Methodology  
The integration of point measurement and surface measurement can not only accurately measure the deformation of a single monitoring point, but also obtain the overall deformation of the slope surface [32; 33; 34; 45]. In order to integrate the advantages of point measurement and surface measurement, an improved point cloud comparison method was proposed. This method used the normal vector of the reference point cloud as the axis to construct a prism, and determined the position of the comparison point cloud by calculating the center of gravity in the prism and extracted the three-dimensional deformation information along the normal direction.  
The main ideas are as follows [33; 46; 47]:  
(1) For any reference point \(i(x,y,z)\), construct a covariance matrix based on the neighborhood point set in the sphere with the reference point as the center and \(R\) as the radius, and find the eigenvector corresponding to the smallest eigenvalue, that is, the normal vector \(N\) of the reference point;  
(2) Construct a prism with the normal vector \(N\) as the axis, \(d\) as the side length, and \(H\) as the height. The prism contains a reference point set and a comparison point set, of which the reference point \(i\) is located in the reference point set;  
(3) Project the comparison point set onto the normal vector \(N\), and calculate the barycentric coordinates of the projected points. The barycentric point is the point of the same name corresponding to the reference point \(i\), and the distance of the point pair of the same name is calculated as the deformation amount of the reference point; and  
(4) Obtain the model parameters with the highest accuracy of slope deformation measurement through model tests. Conduct study on the research object to obtain the amount of slope deformation  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Registration Method** & **Elapsed Time** & **RMSE** \\ \hline K-D tree improved ICP algorithm & 3.575 s & 0.445 mm \\ LM improved ICP algorithm & 5.451 s & 0.987 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Quantitative indicators of point cloud data registration.  
Figure 3: (a) registration results of K-D tree improved ICP algorithm, (b) registration results of LM improved ICP algorithm.  
during the monitoring period based on the optimal parameters. The calculation principle is as shown in Figure 4.  
It is important to note that differences between the reference point cloud and comparison point cloud may be caused by non-slope deformations such as the growth of vegetation, so it is very important to filter the influence of the vegetation on the deformation measurement. An interesting ground filtering method was developed by [PERSON] et al. [48], who proposed a novel filter of LiDAR point clouds based on geodesic transformations of mathematical morphology, where the algorithm made it unnecessary to select different window sizes or determine the maximum window size, which could enhance the robustness and automation for unknown environments. In this paper, this algorithm was adopted in ground filtering before the slope deformation measurement.