## 4 Experiment and Result Analysis
### Quantitative Analysis  
In order to determine the optimal parameters of each detection method, the ROC curves of the above five methods are plotted based on the key obstacle subclass in the training set, as shown in Figure 12. Among them, the main parameters of reference [19] are the obstacle probability threshold. The main parameters of reference [10] are the vertical cut costs used in dynamic programming and the width of the stixels. The main parameters of the OD-PNV, OD-SPH and OD-LSF methods are the width of the stixels and the obstacle probability threshold. The optimal parameters are selected according to the convex hull position of each curve (as shown by the red circle in Figure 12). The detection performance indicators of the five methods in the test set under the optimal parameters are shown in Table 1. By comparing Figure 12 and Table 1, it can be found that the ranking of the five methods according to the performance indicators is completely consistent in the training set and the test set. Table 1 indicates that the three methods proposed in this paper, OD-PNV, OD-SPH and OD-LSF, are superior to the other two methods in terms of the PTPR and PFPR, while OD-LSF achieves the highest PTPR and lowest PFPR, respectively. The indicators of the OD-SPH  
Figure 12: ROC curves. the detection of a complete obstacle class are relatively close. This is because the OD-SPH method is good at detecting obstacles in higher spaces, such as buildings and vegetation, which account for a large number of pixels. In the detection of a key obstacle subclass, the PTPR indicator of the OD-LSF method is significantly better than that of the OD-SPH method, which indicates that the fusion of the two local spatial features improves the detection ability of the OD-LSF method for the key obstacle subclass. The PFPR indicator of the OD-LSF method is obviously superior to the OD-PNV method, which is because the OD-LSF method incorporates the height information of obstacles and corrects the false detection of the OD-PNV method to a certain extent. Reference [19] and the OD-SPH method are relatively close in principle, as both rely on height information to detect obstacles, but the performance indicators of the OD-SPH method are better than reference [19]. This is because the OD-SPH method uses the classification result of the OD-PNV method in its road surface model fitting, which avoids false fitting in scenes with a complex road surface. In some complex traffic scenes, reference [19] relies solely on the height information of the 3D points, so it is possible to fit the false road surface model, which will have a significant impact on the performance indicators. Figure 13 shows the PTPR over PFPR scatter plots of the five methods under the two obstacle classification standards. A high PTPR and low PFPR (upper left corner of the figure) can reflect the best detection performance. It can be seen from the figure that the points of the OD-LSF method under the two obstacle classification standards are closer to the upper left corner of the figure than the other four methods, and the distribution of the points is more concentrated. This indicates that the OD-LSF method not only performs better in terms of its detection performance, but also is stronger than the other methods in terms of its stability. In terms of operating efficiency, the average single-frame running time of reference [19], reference [10], OD-PNV, OD-SPH, and OD-LSF are 203 ms, 175 ms, 209 ms, 214 ms, and \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Key Obstacle Subclass**} & \multicolumn{2}{c}{**Complete Obstacle Class**} \\ \hline
**Method** & **PFPR(\%)** & **PFPR(\%)** & **PFPR(\%)** & **PFPR(\%)** \\ \hline Ref. [19] & 83.3 & 12.2 & 89.4 & 12.2 \\ Ref. [10] & 76.9 & 5.6 & 88.6 & 5.6 \\ OD-PNV & 92.2 & 5.5 & 95.4 & 5.5 \\ OD-SPH & 88.9 & 3.8 & 96.0 & 3.8 \\ OD-LSF & 92.7 & 3.5 & 96.8 & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detection performance indicators of the five methods.