## 2 Data and Method
### Methods
#### 2.2.6 Tree Species Classification  
The Key Points of the Tree Crowns  
Tree species differ significantly in terms of canopy height and growth pattern, and after the segmentation processing, the tree crown points can be classified as a group. From Figure 9, different tree species have different profile structures. In this paper, the profile of the tree crown points is used to get key points which can definitely denote the shapes of the tree crown. In order to get the key points, a Parallel Line Cutting method is used to browse the entire profile points. The details are listed as Figure 10 shows:  
Figure 9: Various tree species with different profile structures. (1) For a given segmented tree point group, draw a vertical line L from the tree top vertex to the ground;  
(2) Taking the treetop as the center, get a profile with a certain width \(D\). the size of \(D\) is related to the average point spacing distance _dis_ of the point cloud, generally \(D=2\)_dis;_  
(3) On the point cloud profile, draw parallel lines along the line \(L\) with a certain spacing \(d\) to obtain the point cloud coordinates of the endpoints within the parallel line interval;  
(4) After the browsing, all the endpoints can be defined as the key points of the tree crown. The Parallel-Line Shape Fitting of the Key Points  
From the Figures 9 and 10, the tree crown can be simplified into a combination of basic shapes such as sectors, isosceles triangles, and rectangles. In other words, all the crown shapes can be fitted to combinations of basic shapes from the key points of the tree crowns. (1) From Section 2.2.5, the treetops and the segmented tree crowns can be obtained. And then in the top view, take the tree top point as the center, the crown length of the tree crown as the profile length, and take \(w\) as the width of the cross-sectional view of the crown, then the profile points of the tree crowns points \(C_{crown-profile}\) can be generated, and all the details are shown in Figure 11.  
(2) The tree crowns points \(C_{crown-profile}\) can be projected onto the plane of the profile plane, and in that way, the 3D points can be transferred to 2D points \(C_{crown-profile}^{2D}\), then a series of excellent algorithms can be used, such as the alpha shapes algorithm [60] which is one of the best algorithms to get the shape of the point set \(\delta\mathcal{C}\) as the Figure 12 shows. In addition, the user can also control the shape \(\delta\mathcal{C}\) of set \(C_{crown-profile}^{2D}\) by adjusting the unique parameter \(\alpha\) of the algorithm. (3) The generation of the key points of the \(\delta\mathcal{C}\). As the Figure 13 shows, select any point A1 of the \(\delta\mathcal{C}\) as the starting point and calculate the distance to the connecting line of the adjacent two points. If the distance \(d\) is bigger than the threshold \(T\), the point is signed as a key point, otherwise it is signed as an un-key point. Keep calculating until all the edge points are judged, then the first turnkey point set is obtained. Use the same method to judge the key points set and keep iterating until the number of key points does not change and finally the key point set of the crown section boundary is obtained. (4) In the sparse northeast forest region of China, airborne LiDAR points data can basically obtain the complete shapes of the tree crowns. Therefore, the shape information of the tree crown can be extracted by obtaining the outer contour of the tree crown key points. In this paper, the parallel line segment length comparison method (PLSM) is used to realize the fitting of the crown shape, and to finally realize the structural composition of the whole crown. The specific steps of PLSM are as follows:  
Figure 10: The profile shapes of the tree crowns. (**a**) triangle. (**b**) sector. (**c**)rectangle. (**d**) The combination of sector and trapezoid from top to bottom. (**e**) The combination of sector and triangle from top to bottom. (**f**) The combination of two triangles from top to bottom.