## 2 Method
### Selection of Variable Factors  
Feature selection plays an important role in machine learning. While the variables obtained in the experiment contain very important classification information, there are some less relevant and redundant information. To avoid the over-fitting problem of the classifier and improve the accuracy and efficiency of the classifier, it is necessary to perform feature selection. There are many current feature selection methods [51; 52]. The advantage of the mRMR [46] algorithm is that it not only considers the correlation between input variables and output variables, but also considers the correlation between each input variable. Through the mRMR algorithm, the feature subset with the largest correlation with the output variable and the smallest correlation with the input variable can be found from the initial input variables. [PERSON] et al. [53] proved by experiments that no matter which criterion is adopted, mRMR has encouraging feature selection results compared with the traditional K-BEST feature selection method. Therefore, we used the mRMR algorithm to screen the obtained nine variable factors (namely, the 3D coordinates of the point cloud, the normal vector of the point cloud in the x-y-z direction, the curvature of the point cloud, the partial height difference of the point cloud, and the height difference of the point cloud filter reference surface).  
The mRMR method is a feature selection method based on mutual information as a subset evaluation criterion, which can effectively measure the correlation between features and categories and the redundancy between feature sets. One goal of feature selection is to find a subset of features \(S\) that has the highest correlation with class \(c\) and contains \(m\) features, called max-relevance. Another purpose of feature selection is to reduce the redundancy between features in the feature subset \(S\), called minimum redundancy.  
The correlation between feature subset \(S\) and class \(c\) is measured by Equation (1). The larger the value of \(D\), the higher the relevance between the feature subset and class \(c\); The redundancy of the features in the feature subset \(S\) is calculated by Equation (2). The smaller the value of \(R\), the less redundancy between feature subsets.  
\[\max D(S,c),\quad D=I(\{x_{i},i=1,...,m\};c) \tag{1}\]  
\[\min R(S),\ R=\frac{1}{|S|^{2}}\sum_{x_{i},x_{i}\in S}I(x_{i},x_{j}) \tag{2}\]  
Combining the above two indicators, the standard for measuring the quality of feature subsets under the mRMR framework is determined by Equation (3). The higher the value of \(\varnothing\), the higher the evaluation of the subset of features.  
\[\max\varnothing(D,R),\varnothing=D-R \tag{3}\]  
According to the evaluation results, each variable factor is scored and sorted from high to low. Figure 3 shows the scores of all variable factors, where the 3D coordinates x, y, and z of the point cloud have scores of 0.0463, 0.082, and 0.086, respectively, the point cloud y-normal vector score is 0.1554, the point cloud partial height difference score is 0.2923, the score of the cloud x-normal vector is 0.3676, the score of the point cloud curvature is 0.3725, the score of the point cloud z-normal vector is 0.3771, and the score of the point cloud height difference of filtering reference surface is 0.5218.  
Selecting \"excellent\" variable factors from the candidate variable factors can improve model performance and the accuracy and efficiency of filtering. According to the score ranking of each variable, the scores of the three variable factors of the 3D coordinates x, y, and z of the point cloud are all less than 0.1, and the impact on the final result is minimal. Therefore, these three variable factors are eliminated, and the remaining six variable factors are retained.