## 3 Experiment and Result
### Tree Species Classification  
This article uses structural and geometric information of each individual tree to determine the tree species classification. In the test site, there are mainly six kinds of trees, including pine, birch, cedar, Tsubaki, shrub, and others, and the details of the training plots are listed in Table 2. In this paper, several typical trees of each type are selected to get firsthand geometry information, as Table 4 shows. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Plot** & \multicolumn{2}{c}{\(d=1\), \(H_{T}=1\)} & \multicolumn{2}{c}{\(d=1.5\), \(H_{T}=1\)} & \multicolumn{2}{c}{\(d=2\), \(H_{T}=1\)} & \multicolumn{2}{c}{\(d=2.5\), \(H_{T}=1\)} & \multicolumn{2}{c}{\(d=1\), \(H_{T}=1.5\)} & \multicolumn{2}{c}{\(d=1\), \(H_{T}=2\)} & \multicolumn{2}{c}{\(d=1\), \(H_{T}=2.5\)} & \multicolumn{2}{c}{**TTN**} \\ \cline{2-13}
**ID** & **RTN** & **CTN** & **RTN** & **CTN** & **RTN** & **CTN** & **RTN** & **CTN** & **RTN** & **CTN** & **RTN** & **CTN** & **RTN** & **CTN** \\ \hline
1 & 357 & 125 & 167 & 121 & 110 & 109 & 73 & 109 & 307 & 121 & 224 & 121 & 187 & 106 & 118 \\ \hline
2 & 168 & 96 & 97 & 92 & 91 & 91 & 91 & 91 & 142 & 96 & 115 & 96 & 83 & 81 & 90 \\ \hline
3 & 151 & 58 & 73 & 51 & 45 & 45 & 45 & 45 & 123 & 54 & 107 & 54 & 67 & 45 & 50 \\ \hline
4 & 153 & 84 & 81 & 75 & 68 & 68 & 46 & 46 & 117 & 77 & 89 & 71 & 69 & 63 & 74 \\ \hline
5 & 45 & 43 & 42 & 42 & 39 & 39 & 27 & 27 & 44 & 43 & 37 & 35 & 31 & 29 & 42 \\ \hline
6 & 131 & 71 & 71 & 67 & 67 & 67 & 41 & 41 & 114 & 68 & 67 & 61 & 43 & 37 & 66 \\ \hline
7 & 132 & 68 & 66 & 65 & 66 & 65 & 45 & 45 & 121 & 66 & 79 & 57 & 48 & 41 & 65 \\ \hline
8 & 249 & 121 & 125 & 119 & 107 & 107 & 71 & 71 & 179 & 118 & 129 & 109 & 97 & 92 & 116 \\ \hline
9 & 165 & 67 & 83 & 59 & 54 & 54 & 38 & 38 & 125 & 61 & 103 & 53 & 59 & 49 & 58 \\ \hline
10 & 205 & 110 & 117 & 105 & 97 & 97 & 65 & 65 & 165 & 105 & 133 & 93 & 79 & 76 & 102 \\ \hline \hline \end{tabular} Note: RTN: Rough Tree Number, CTN: Calculated Tree Number, TTN: True Tree Number.  
\end{table} 
Table 3: The rough tree number and calculated tree number in each plot with different values of parameters \(d\) and \(H_{T}\). From Section 2.2.6, in the first stage, the Birch, Cedar, Shrub can be classified using the basic shapes. And in the second stage, the Pine and Tsubaki can be ruled out using the \(R_{triangle}\) as Figure 18 shows. From the samples, pine usually has a big \(R_{triangle}\), because the tree crown is usually exceedingly high. In the test site, the value ranges from 2.1 to 4.7, but we set the range from 2 to 5. For the Tsubaki, the range is not so big, but from 0.8 to 1.4. Here, we set it as 0.5 to \begin{table}
\begin{tabular}{c c c c c} \hline
**Tree Species ID** & **Sample Number** & **Basic Shape Type** & **Parameter Type** & **Parameter Range** \\ \hline
01-Pine & 20 & Triangle & \(R_{triangle}\) & (2.1, 4.7) \\ \hline
02-Birch & 10 & arc and trapezoid & — & — \\ \hline
03-Cedar & 10 & arc and rectangle & — & — \\ \hline
04-Tsubaki & 8 & Triangle & \(R_{triangle}\) & (0.8, 1.4) \\ \hline
05-Shrub & 15 & Arc & — & — \\ \hline \end{tabular}
\end{table} 
Table 4: The shape and parameters of the tree samples. Figure 17: Single tree segmentation results of ten plots. Figure 18: The definition of the \(R_{triangle}\). 1.5. Then, we classify the triangle type trees which depends on the value of the \(R_{triangle}\)-Accuracy evaluation indicators include the following:  
Classification accuracy: the ratio of the correctly classified tree number of a certain species to the total number of trees of that species. Type I error: Proportion of trees not belonging to class A tree species classified to class A tree species. Type II error: Proportion of trees belonging to class A tree species not classified to class A tree species.