## 2 Materials and Methods
### Construction of the MSMF-PointNet Model  
#### 2.3.1 MSMF-PointNet Deep Neural Network  
Unlike optical imagery, whereby a regular grid renders it convenient for convolution and automatic feature extraction in an end-to-end framework, a LiDAR point cloud is disordered and irregular, which must be overcome in the design of the DNN. PointNet defines the MLP-Max operation in a spherical neighborhood to extract point features. A spherical neighborhood, also known as the r-neighborhood, contains all points in a sphere with a point as the center and r as the radius. In MLP-Max operations, a multilayer perceptron (MLP) is operated to extract a feature for every point, and then max pooling is used to summarize the extract. As mentioned in Sections 2.1 and 2.2, we took multidimensional features for each point, used these to replace single features as the input of the deep neural network for feature learning, and took radius R as the scale parameter to construct the multiscale structure. In this section, a multiscale and multi-neighborhood MSMF-PointNet classification model is constructed on the basis of the PointNet structure to improve the input feature dimension of the model and extract multiscale neighborhood point-cloud features for ground object classification. In order to improve the training efficiency of the network, the 16-dimensional features are divided into three parts. In the first part, the XYZ information and RGB information of the point cloud are input into the improved PointNet network. The second part and the third part are the five features obtained when the radius of the spherical neighborhood was 0.8 and 1.2, respectively, and the eight-dimensional features of the XYZ information of the point cloud are input into the two additional small networks. There are some specific ideas for improvement. Aiming at the problem of increasing the dimensions of the fusion point-cloud feature space, the input transformation matrix dimension is adjusted to increase the number of channels so that the matrix is changed from originally processing three-dimensional feature vectors to processing the fusion of six-dimensional and eight-dimensional feature vectors. In view of the increase in data volume brought by the expansion of the feature space of fusion point-cloud data, the point cloud's depth features are fully extracted by deepening the number of network layers of the MLP layer. In order to solve the problem of lack of local neighborhood features, two small PointNet feature extraction networks were built using as inputs the point-cloud features calculated in the spherical neighborhood, and multi-neighborhood point-cloud features of different scales were extracted. A block diagram of the MSMF-PointNet network structure is shown in Figure 2.  
Figure 2: Architecture of MSMF-PointNet. (R = 0.8 m and R = 1.2 m: the radius of the spherical neighborhood is 0.8 and 1.2 respectively; R, O, P, L, and V: roughness, omnivariance, planarity, linearity, and verticality). The concrete measures to construct the MSMF-PointNet network were as follows: first, the original input transformation matrix T-Net(3) was replaced with T-Net(6) and T-Net(8). The new networks can carry out more spatial transformations of the fusion point-cloud data. Three convolution layers were added to the MLP layer of the original global feature extraction part to increase the depth of the feature extraction. Two multi-feature extraction networks of different scales, each being a small PointNet network, were added to the original PointNet network. The network structure is shown in the dotted box in Figure 2.  
At each scale, a five-layer small MLP network and maxpooling structure were set, and a 256-dimensional feature vector was obtained as the local point-cloud feature through pooling. The two-scale neighborhood features were connected to the original single-point and global features extracted by PointNet through the full connection layer to obtain the multiscale neighborhood feature vectors.