## 3 Experimental Results and Analysis
### Experimental Comparison and Analysis  
In order to verify the performance of the proposed algorithm, we compare it with the other seven methods shown in Table 2. Method 1 is the proposed method, which uses the features without NAD and LSH. Method 2 uses the \(F_{z}\)+\(F_{NAD}\)+\(F_{LSH}\)+\(F_{cov}\)+\(F_{plane}\) feature fusion in single-scale without a post-processing optimization. Method 3 uses the single-scale feature and multi-scale pyramid optimization. Method 4 is the algorithm proposed in [24]. In this method, each feature uses geometry, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scene**} & \multicolumn{4}{c}{**Training Points**} & \multicolumn{4}{c}{**Test Points**} \\ \cline{2-7}  & **Tree** & **Building** & **Car** & **Tree** & **Building** & **Car** \\ \hline Scene 1 & 68,802 & 37,128 & 5380 & 213,990 & 200,549 & 7816 \\ Scene 2 & 39,743 & 64,952 & 4584 & 73,207 & 156,186 & 7409 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experimental dataset. Figure 4: The training data of the ALS points. (**a**) scene 1, and (**b**) scene 2. (The figures are captured from the ALS points shown in Cloudcompare ([[http://www.cloudcompare.org/](http://www.cloudcompare.org/)]([http://www.cloudcompare.org/](http://www.cloudcompare.org/))). The red points are cars, green points are buildings and blue points are trees.) strength, and statistics information. Following this, the JointBoost method is used to select features and classify points. Method 5 is the classification method based on the multi-scale Spin Image feature and \(F_{cov}\) feature fusion used in Ref [23]. Method 6 [25] constructs a multilevel point set using a linear transformation, and it uses Spin Image and \(F_{cov}\) features. Following this, K-means is used to construct an LDA (Latent Dirichlet Allocation) model of a multilevel point set dictionary. Method 7 [23; 26; 27] constructs a multilevel point set using an exponential transformation. The Spin Image and \(F_{cov}\) features are used for dictionary learning, constructing an LDA model of point sets. Accuracy, precision, and recall are often used to evaluate the effect of a point cloud classification [27]. The precision rate is the proportion of true positive samples in a positively predicted sample. The recall rate is the proportion of positive samples that are predicted to be successful in the actual positive samples. The accuracy rate is the ratio of all the correctly predicted samples in relation to the overall samples. In order to consider both \(P_{a}\) (precision rate) and \(R\) (recall rate), \(F_{1}\)-score values (such as Equation (28)) are generally used to represent the classification quality of the scene. In order to better evaluate the effects of each algorithm, we use the above metrics to evaluate the classification performance. \[F_{1}-score=\frac{2(R\times P_{a})}{R+P_{a}} \tag{28}\]  
The classification results of our method and of other comparison methods on scene 1 and scene 2 are shown in Table 3. Table 3 lists the precision, recall, accuracy and \(F_{1}\)-score statistics for the eight methods in the two scenes. It can be seen from Table 3 that the comparison between the proposed method and Method 1 shows that the accuracy of the proposed method has significantly improved. It also shows that the proposed NAD and LSH features have certain effects. By comparing Method 2 and Method 3, the proposed multi-scale pyramid optimization algorithm can effectively improve the classification accuracy. Comparing the proposed method with Method 3, the proposed multi-scale strategy has a significant effect on the improvement of the classification results. In addition, the proposed method is compared with the methods given in other references. Method 4 and Method 5 classify the point cloud based on the single-point. Method 6 and Method 7 classify the point cloud based on the point set (object). It can be seen from the comparison of Table 3 that the proposed method has a high accuracy rate as a whole, and that it also maintains a high recall rate.