## 2 Method
### Point Feature Extraction
#### 2.1.1 Feature Description  
1. Elevation feature  
The height is a very intuitive feature in a 3D point cloud. Generally speaking, points with large height are buildings, trees or objects with larger elevation values in the real world. When the elevation value is small, the probability is greater if the point is a vehicle point. Thus, the elevation feature is set to:  
\[F_{z}=[Z_{i},\ \frac{1}{Z_{i}}] \tag{1}\]  
where \(Z_{i}\) is the distance of the \(i\)-th point from the estimated ground to the elevation value. 2. Normal angle distribution histogram  
In the large scale scene, the normal direction of different objects has obvious differences. For artificial objects, such as buildings and vehicles, since the surface is relatively regular, almost all points are in the same direction, pointing in the direction of the vertical plane. However, due to the scattered distribution of the whole point cloud, the normal direction of the point cloud has a large scattered nature, and the direction does not point to a fixed direction in a uniform way. Therefore,  
Figure 1: Flowchart of the proposed method. NAD: normal angle distribution histogram;LSH: latitude sampling histogram; SVM: Support Vector Machine. we calculate the histogram of each point and its own normal angle distribution value in the local neighborhood point set to express the relationship between the normal of the point and the normal of the points in the neighboring region. The angle between the two normal vectors in three-dimensional space should be between \([0,\pi]\). But considering that the normal of the point on the plane can have opposite directions when the angle is larger than \(\pi/2\), the corresponding angle is set to \(\pi-\pi/2\). Following this, the angle of the normal vectors is defined as \([0,\pi/2]\). Considering efficiency and resolving power, we divide this interval into equal \(D_{n}\) parts, that is, construct a \(D_{n}\) dimensional histogram. After this, the number of points falling within each cell is taken as the value of the interval in the histogram. Finally, the normalization process is performed to form a histogram of the normal angle distribution, called NAD. This feature can distinguish different classes of points based on the normal angular distributions. The specific calculation formulas are as follows:  
\[\Delta=\frac{\pi/2-0}{D_{n}} \tag{2}\]  
\[\theta_{j} =\text{a}\cos\left(v\cdot v_{j}\right) \tag{3}\] \[h(x_{i})=\frac{n(i*\Delta\leq\theta_{j}\leq(i+1)*\Delta)}{N}\;(i =1,\ldots,\;D_{n})\] (4) \[F_{NAD}=[h(x_{1}),h(x_{2}),\ldots,h(x_{D_{n}})] \tag{5}\]  
where \(v\) and \(v_{j}\) represent the normal vectors of the current point and the \(j\)-th neighbor point, respectively. \(\text{a}\cos(\cdot)\) represents the inverse cosine function. \(N\) represents the number of neighbors for the current point. \(n(i*\Delta\leq\theta_{j}\leq(i+1)*\Delta)\) denotes the number of points for the normal angle at the range \([i*\Delta,(i+1)*\Delta]\). \(F_{NAD}\) denotes the final normal angle eigenvalue vector of the normal angle distribution. The histogram of the normal angle distributions for the randomly selected building points and tree points are shown in Figure 2.  
to distinguish different classes of points according to the distribution of neighborhood points in the latitude direction. The LSH has the advantages of anti-occlusion, without interference from the local coordinate system, as well as high efficiency. In this paper, \(D_{l}\) spaces are equally divided along the latitude direction. Following this, the number of points falling into each cell is counted to form a feature vector of the \(D_{l}\) dimension. The specific calculation formulas are:  
\[\Delta=\frac{\pi-0}{D_{l}} \tag{6}\]  
\[\theta_{j} =\text{a}\cos\bigl{(}z\cdot\bigl{(}p_{j}-p\bigr{)}\bigr{)} \tag{7}\] \[f(x_{i})=\frac{n\bigl{(}i*\Delta\leq\theta_{j}\leq(i+1)*\Delta \bigr{)}}{N}\ (i=1,\ldots,D_{l})\] (8) Figure 1:0  
where \(p\) and \(p_{j}\) represent the three-dimensional coordinates of the current point and its \(j\)-th neighbor point, respectively.