## 2 Materials and Methods
### Selection of Multi-Neighborhood Features  
At present, the features applied to airborne LiDAR point-cloud classification can be divided into three categories: features based on echo signals, features based on descriptors, and geometric features. Relatively speaking, in the current point-cloud classification research, geometric features have been proven to be the most effective and have seen the most use [25]. Unlike eigenvectors, eigenvalues have good rotationally invariant properties [26]. In order to allow the network to learn more features and improve the classification accuracy of the network, four geometric features based on point clouds were selected in addition to the basic point-cloud features (i.e., XYZ and RGB). At the same time, we prevent the network from learning less-than-effective features due to feature redundancy, which leads to the non-convergence of the network and the establishment of an effective classification model. The specific meanings and formulas used in the calculations are shown in Table 1.  
The roughness is the ratio between the surface area of a given region and its projected area. The roughness of trees, for example, is significantly higher than that of manmade structures. \(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) are eigenvalues of the point cloud, where \(\lambda_{1}\geq\lambda_{2}\geq\lambda_{3}\). An analysis of the eigenvalues and eigenvectors can often provide important information for extraction decisions. According to the points in the neighborhood, the covariance matrix of the center point was calculated, and then the eigenvalues of the points were obtained [27]. On the basis of these eigenvalues, four kinds of features can be calculated, namely, the sum of omnivariance (\(O_{\lambda}\)), planarity (\(P_{\lambda}\)), linearity (\(L_{\lambda}\)), and verticality (\(V_{\lambda}\)). \(O_{\lambda}\) has a strong ability to describe the degree of fluctuation in a point-cloud surface. Generally speaking, complex surfaces have higher \(O_{\lambda}\) values. The omnivariances of trees and grass are higher than those of manmade surfaces and buildings. \(P_{\lambda}\) is a measurement of the planar characteristics of the point cloud. It can effectively represent the level of the fitted surface in the neighborhood at a given point. A flatter surface is characterized by a higher \(P_{\lambda}\). For example, the flatness of an artificial road surface is significantly higher than that of a tree-lined surface. \(L_{\lambda}\) denotes the degree of linearity of the point cloud. Power lines and edges of buildings have obvious linear structures, and the linearities of these points are characterized by high values. \begin{table}
\begin{tabular}{c c c c} \hline
**Feature Type** & **Name** & **Formula** & **Explanation** \\ \hline \multirow{3}{*}{Basic features} & XYZ & / & The basic features of point cloud are obtained \\ \cline{2-4}  & RGB & / & through fusion of the point cloud and image. \\ \hline \multirow{3}{*}{Common features} & \multirow{3}{*}{Roughness} & / & The roughness is the ratio between the surface area of a given region and its projected area. \\ \hline \multirow{5}{*}{Eigenvalue-based features} & Omnivariance & \((\lambda_{1}\cdot\lambda_{2}\cdot\lambda_{3})^{1/3}\) & Omnivariance describes the surface \\  & & & undulation of the point cloud. \\ \cline{2-4}  & Planarity & \((\lambda_{2}-\lambda_{3})/\lambda_{1}\) & Planarity denotes the evenness of the fitted surface in the neighborhood at this point. \\ \cline{1-1} \cline{2-4}  & Linearity & \((\lambda_{1}-\lambda_{2})/\lambda_{1}\) & The linearity of the point cloud. \\ \cline{1-1} \cline{2-4}  & & & Verticality describes the fitting at a point \\ \cline{1-1} \cline{2-4}  & Verticality & \(1-|Z\cdot N|\) & \(1-|Z\cdot N|\) & \\ \cline{1-1} \cline{2-4}  & & & unit vector in the vertical direction, and N is \\ \cline{1-1} \cline{2-4}  & & & the normal vector of this point. \\ \hline \end{tabular}
\end{table} 
Table 1: Features for classification.