## 2 Method
### Experimental Data  
Considering that different terrains may affect the filtering results, in order to ensure the terrain applicability of this filtering method, we used three groups of different types of forest data to train the filtering model, and each group consists of three data. Group I contains data 1-3. The topographic features of this group are flat terrain or gentle slope, and no steep slopes. Group II includes data 4-6. The topographic features of this group are with steep or terraced slopes. Group III includes data 7-9. The topographic features of this group are high and steep slopes. The LiDAR data used in this method comes from the open topography website. Data 1, data 4, and data 7 are from the dataset \"Hydroologic Effects of Forest Restoration, WA 2021\". The study area of this LiDAR dataset consists of sections located northwest of Ellensburg, WA, and covers approximately 62.7 km\({}^{2}\). Data 2, data 3, and data 5 are from the dataset \"Mapping the Kaibab Plateau, AZ\". This dataset provides LiDAR data for portions of the Kaibab National Forest and Grand Canyon National Park on the Kaibab Plateau. The study area covers an area of about 1882.3 km\({}^{2}\). Data 6, data 8, and data 9 are from the dataset \"Study in Erosion Response: Horse Linto, CA 2019\". The study area of this LiDAR dataset covers approximately 63 km\({}^{2}\) near Horse Linto, in Trinity National Forest, California. Information about the collected data can be found in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Ground Points** & **Non-Ground Points** & **Total Number** & **Errors** \\ \hline Ground points & \(a\) & \(b\) & \(e=a+b\) & \(b/e\) (T.I) \\ Non-ground points & \(c\) & \(d\) & \(f=c+d\) & \(c/f\) (T.II) \\ Total number & & & \(n=e+f\) & \((b+c)/n\) (T.E.) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definition of filtering error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Group** & **Number of Points** & **Feature** & **Dataset Short Name** \\ \hline \multirow{4}{*}{I} & data 1 & 14,745,103 & & WA21\_Lumbrazo \\  & data 2 & 10,727,129 & Flat terrain or gentle slope, no steep slopes & AZ12\_USFS \\  & data 3 & 9,803,227 & & AZ12\_USFS \\ \cline{2-5}  & data 4 & 9,403,664 & & WA21\_Lumbrazo \\ II & data 5 & 13,036,927 & With steep or terraced slopes & AZ12\_USFS \\  & data 6 & 10,348,378 & & CA19\_Feed \\ \cline{2-5}  & data 7 & 9,772,423 & & WA21\_Lumbrazo \\ III & data 8 & 8,343,649 & High and steep slopes & CA19\_Feed \\  & data 9 & 11,162,971 & & CA19\_Feed \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic information of the collected data. The filtering verification results of Group I are shown in Figure 4. The terrain in this group is relatively flat, and some areas may have some gentle slopes. The filtering accuracy of data 1 is 92.18%, the filtering accuracy of data 2 is 82.25%, and the filtering accuracy of data 3 is 81.19%; The filtering verification results of Group II are shown in Figure 5. This group of data includes gentle slopes and steep slopes, and the overall terrain presented is relatively simple. The filtering accuracy of data 4 is 91.56%, the filtering accuracy of data 5 is 81.69%, and the filtering accuracy of data 6 is 83.32%; The filtering verification results of Group III are shown in Figure 6. The terrain of this group is steep slopes and high steep slopes, with some ravines and complex terrain. The filtering accuracy of data 7 is 94.32%, the filtering accuracy of data 8 is 89.03%, and the filtering accuracy of data 9 is 90.25%. It can be seen from the filtering result graph that this method can achieve good performance in Group I-III, and the filtering accuracy of each data can reach more than 80%. Especially in Group III, with steep slopes and high steep slopes, the classification effect of filtering is excellent. At the same time, judging from the misclassification of each result map, the misclassified point clouds mainly exist near the ground points, which are very close to the terrain surface.