## 4 Experiments
### Performance Evaluation  
#### 4.2.1 Verification Experiment  
Figure 16 first shows the three-dimensional point cloud map of a test scene and the ground-filtering effect of the ROI. Our method performs well in mapping the scene and filtering ground points within the ROI. The convex hull detection of the obstacle vehicles and the marking of vacant parking spaces are illustrated in Figure 17. The red convex hull line in Figure 17 is a schematic representation of obstacle marking. Figure 17 shows the parking space marking result for perpendicular parking spaces, while Figure 17 depicts the marking result for parallel parking spaces. In Figure 17, the green area represents the free space between perpendicular obstacle vehicles, and the yellow area indicates the marked perpendicular parking space. In Figure 17, the green area represents the free space between horizontal obstacle vehicles, and the yellow area indicates the marked horizontal parking space. The number 0 denotes a perpendicular obstacle vehicle, and the number 1 denotes a parallel obstacle vehicle.  
Figure 16: 3D point cloud map of a test scene and ground filtering of the ROI. (**a**) 3D point cloud map of a test scene; (**b**) 3D point cloud map of a test scene with an ROI box; (**c**) Before filtering out ground points in the ROI; (**d**) After filtering out ground points in the ROI.  
Figure 15: Examples of parking scenes in nuScenes [15]. (**a**) A parking lot in Queenstown, Singapore; (**b**) A on-street parking area at Boston Seaport.  
The performance is evaluated using the following parameters and equations:  
\[Precision=\frac{TP}{TP+FP}\, \tag{31}\]  
\[Recall=\frac{TP}{TP+FN}=\frac{TP}{GT}\, \tag{32}\]  
\[F1\ Score=\frac{2 Recall\times Precision}{Recall+Precision} \tag{33}\]  
Table 5 shows the performance evaluation results of the proposed parking space annotation method based on Lidar and IMU. In Table 5, GT, TP, and FP represent the number of existing parking spaces, the number of correctly detected parking spaces, and the number of incorrectly detected parking spaces, respectively. As shown in Table 5, the mean precision and recall of the proposed method are 98.89% and 98.79%, respectively. Compared to the 95.2% precision and 93.6% recall reported in the literature [19], the performance is greatly improved.  
Figure 17: Schematic diagram of the annotation for obstacle vehicles and parking spaces. **(a)** Perpendicular obstacle vehicles and perpendicular parking spaces; **(b)** Parallel obstacle vehicles and parallel parking spaces. \"0\" recognized the classification label of perpendicular parking mode; And \"1\" represented horizontal parking mode.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Test Group**} & \multicolumn{1}{c}{**GT**} & \multicolumn{1}{c}{**TP**} & \multicolumn{1}{c}{**FP**} & \multicolumn{1}{c}{**Precision (\%)**} & \multicolumn{1}{c}{**Recall (\%)**} & \multicolumn{1}{c}{**F1 Score (\%)**} \\ \hline \multirow{5}{*}{Scenario} & Site 1 (1 st loop) & 256 & 252 & 3 & 98.82 & 98.44 & 98.63 \\  & Site 1 (2 nd loop) & 256 & 252 & 4 & 98.44 & 98.44 & 98.44 \\  & Site 2 & 107 & 105 & 2 & 98.13 & 98.13 & 98.13 \\  & Site 3 & 279 & 278 & 1 & 99.64 & 99.64 & 99.64 \\  & Site 4 & 91 & 90 & 1 & 98.90 & 98.90 & 98.90 \\ \hline \multirow{3}{*}{Type of Parking Slots} & Parallel & 107 & 105 & 2 & 98.13 & 98.13 & 98.13 \\  & Perpendicular & 740 & 732 & 7 & 99.05 & 98.92 & 98.98 \\ \cline{1-1}  & Angled & 142 & 140 & 2 & 98.59 & 98.59 & 98.59 \\ \hline \multicolumn{2}{c}{Total Number and Average Score} & 989 & 977 & 11 & 98.89 & 98.79 & 98.57 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parking space detection performance of the proposed method.