## 2 Method
### Point Feature Extraction
#### 2.1.1 Feature Description
\(z=(0,0,1)\) represents the unit vector of the positive direction of the \(z\) axis. \(n(i*\Delta\leq\theta_{j}\leq(i+1)*\Delta)\) represents the number of points in \([i*\Delta,(i+1)*\Delta]\) of the neighborhood points along the latitudinal direction. \(F_{LSH}\) represents the final feature vector of LSH. The LSHs of the randomly selected building points and tree points are compared, as shown in Figure 1:1  
4.Convariance feature  
First, a covariance matrix for the selected point neighborhood is constructed. After this, eigenvalues of the covariance matrix are calculated as: \(\lambda_{2}\geq\lambda_{1}\geq\lambda_{0}\geq 0\), and the corresponding eigenvectors are calculated as: \(v_{2},v_{1},v_{0}\). Here, the covariance feature (CF) is obtained according to the relationship among the eigenvalues, as follows:  
Sum of eigenvalues:  
Figure 1:2  
Full variance:  
Figure 1:3  
Anisotropy:  
Figure 1:4  
Planarity:  
Figure 1:5  
Figure 1:6 Latitudinal sampling histogram. (**a**) Latitudinal sampling histogram of a building point. (**b**) Latitudinal sampling histogram of a tree point. Linearity: Figure 1:7 (14) Sphericity: Figure 1:8 (15) Following this, the final total covariance feature is: \(F_{\rm cov}=\left[F_{sum},F_{omnt},F_{ani},F_{pla},F_{lint},F_{sph}\right]\). 5. Plane point ratio  
In outdoor large scale scenes, the classes of objects are complex and the surface shapes are also different. However, a considerable part of the surface of artificial objects exhibits planar characteristics, such as buildings, vehicles, etc. Meanwhile vegetation does not have planar characteristics, so the plane point ratio of the local point cloud can be used as a local feature to classify point clouds. The covariance feature can also reflect the planar characteristics to a certain extent, but it is greatly interfered by noise. For this reason, the Random Sample Consensus (RANSAC) [21] is employed to fit the local neighborhood of the selected point. After this, the ratio of the plane points, called PPR (Plane Point Ratio), is calculated. RANSAC is a method used to find the subset of data that is the best match for the model from the data set with random samples that are noisy but sufficient. The points matched with the model are called the inner points, and the points unmatched with the model are called the outer points. The plane is fitted using RANSAC as follows. (1) Select three points randomly from all the neighborhood points and calculate the current model parameters. The model is as follows:  
Figure 1:9  
(2) Determine whether each point is an inlier, and then determine the inlier rate \(\omega\) of the current model:  
\[J_{i}=\left\{ \begin{array}{ll}1,&\quad d_{i}\leq T_{d}\\ 0,&\quad d_{i}>T_{d}\end{array} \right. \tag{17}\]  
\[\omega=\frac{1}{N}\sum_{i=1}^{N}J_{i} \tag{18}\]  
where \(d_{i}\) is the distance from the \(i\)-th point to the plane. \(T_{d}\) is a fixed threshold. \(J_{i}\) indicates whether it is an inlier or not. \(N\) is the number of neighborhood points. (3) If the current inlier rate is larger than the previous optimal inlier rate, the optimal inlier rate is updated. (4) To find the optimal model, repeat steps (1) to (3) \(k\) times until the probability reaches \(P\):  
\[1-P\leq\left(1-\omega^{3}\right)^{k} \tag{19}\]  
The termination condition is:  
\[k\geq\frac{\log(1-P)}{\log(1-\omega^{3})} \tag{20}\]  
When the RANSAC iteration is completed, the optimal inlier rate is the ratio of the plane points: \(F_{plane}=[\omega]\).