## 5 Experiments and Discussion
### Experiment Comparison of Different Devices  
In order to evaluate the local accuracy of the 3D point cloud map, this paper compares it with manual meter scale measurements and a RoboSense RS-Ruby multi-beam lidar (80-line lidar) based on the LIO-SAM framework in three different scenes. LIO-SAM, the mainstream of current reconstruction methods, is obviously superior to other methods in the field of outdoor reconstruction [9; 35; 36]. Figure 7 shows several maps of a single tree, a row of trees, and a part of the forest area using different devices. This paper takes the measurement values from the manual meter scale as the real values \(D\) and the measurement values from the two other devices as the measurement results \(D_{i}\). The absolute errors caused by the difference between \(D\) and \(D_{i}\), compared with the real values, are taken as the relative errors of the construction of mapping \(\delta\):  
\[\delta=\frac{|D_{i}-D|}{D}\times 100\% \tag{20}\]  
In the measurement of a single tree, this paper collects the height and the diameter of the tree at 1.25 m, 1.58 m, and 1.86 m from the root of the ground using the different devices. The measurement data are shown in Table 1. Analyzing the data shows that the relative error of the method proposed in this paper is 3.66%, and the relative accuracy can reach 96.34%. Figure 5: The 3D point cloud densification and loop closure correction: (**a**) sparse point cloud; (**b**) dense point cloud; (**c**) dense point cloud loop closure correction. Figure 6: The 3D forest point cloud map of a complex scene. Diameter at breast height (DBH) is the most direct factor reflecting tree growth. In order to further evaluate the measurement accuracy of DBH, this paper adopts circle fitting [37] to extract the tree diameter, as shown in Figure 8a. For better DBH estimates, 10 cm-thick sections are selected at heights of 1.25 m, 1.58 m, and 1.86 m, as shown in Figure 8b. We measure different DBH values of 20 trees in the forest area and preprocess the data to eliminate outliers. We use the RMSE, bias, and Pearson's \(r\) parameters for accuracy assessment. The results are shown in Table 2. The average RMSE of DBH is 4.35 cm in the reconstruction with the single-line lidar compared with the real values, which is 2 cm different from that of the multi-beam lidar. The bias values for the DBH estimations are also presented in Table 2. They are 0.476 cm and \(-\)0.273 cm for the multi-beam lidar and single-line lidar, respectively. The average values close to zero show that the DBH estimations are almost unbiased. Pearson's \(r\) represents the correlation between the estimated and the true values of DBH. It is obvious that they all have a high correlation. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**A Single Tree**} & \multicolumn{2}{c}{**The Diameter at 1.25 m**} & \multicolumn{2}{c}{**The Diameter at 1.58 m**} & \multicolumn{2}{c}{**The Diameter at 1.86 m**} & \multicolumn{2}{c}{**The Height**} & \multicolumn{2}{c}{**Average Error**} \\ \cline{2-10}  & \(D_{i}\) **(m)** & \(\delta\) **(\%)** & \(D_{i}\) **(m)** & \(\delta\) **(\%)** & \(D_{i}\) **(m)** & \(\delta\) **(\%)** & \(D_{i}\) **(m)** & \(\delta\) **(\%)** & \(\delta\) **(\%)** \\ \hline Real value & 1.16 & 0 & 1.13 & 0 & 1.06 & 0 & 4.38 & 0 & 0 \\ \hline Multi-beam lidar & 1.18 & 1.72 & 1.11 & 1.77 & 1.04 & 1.89 & 4.45 & 1.60 & 1.75 \\ \hline Single-line lidar & 1.20 & 3.45 & 1.17 & 3.54 & 1.02 & 3.77 & 4.21 & 3.88 & 3.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measurement data of a single tree. Figure 8: Cross-sections of point cloud maps: **(a)** circle fitting; **(b)** 10 cm-thick sections. Figure 7: Accuracy comparison of 3D point cloud reconstruction. For tree spacing in a large-scale forest area, this paper selects a row of 10 trees with different spacings to measure the distance between adjacent trees.