## 5 Discussion  
In the local dataset verification experiment of the proposed algorithm, Table 5 shows instances of incorrect annotations in some parking space detection results. Through data analysis, two main reasons for these discrepancies have been identified. Firstly, mis-annotations of parking spaces can occur due to discrepancies between actual parking space sizes and preset parameters. For instance, when there are two parking spaces, but the planned parking space size is larger, exceeding the preset parameters, the system may erroneously recognize it as three parking spaces. Secondly, irregular parking behaviors by vehicle owners can also contribute to mis-annotations. For example, in a perpendicular parking slots scenario, two cars parked relatively far apart might leave a space in the middle that meets the preset parking space size, leading the system to detect it as another potential parking spot, resulting in an incorrect count of three parking spaces. Similarly, in a parallel garage setup, two mini cars parked at the ends of adjacent spaces with a space in-between might be interpreted by the system as another available parking space. Thus, the standardization of vehicle parking by drivers has a significant impact on the accuracy of this detection method. However, errors resulting from these issues typically fall within the acceptable margin of error for vehicle constraints. In the comparative experiment, it was observed that low-lying obstacles have a significant impact on both the proposed algorithm and the method described in the literature [19]. As illustrated in Figure 19, a scene with curbstones in a parking lot from the nuScenes dataset highlights this issue. Referencing Figure 18a, the proposed algorithm detects vehicles using point clouds and utilizes gaps between vehicles to identify free spaces. However, without distinguishing curbstone point clouds, all gaps meeting vehicle size criteria are erroneously identified as free spaces, leading to increased false detections. In contrast, Figure 18b depicts the method from the literature [19], which screens out obstacles within parking slots after determining them, removing detection boxes containing obstacle point clouds. This approach, while reducing false detections, also increases missed detections of obstacles, thereby compromising the robustness of downstream parking functions. Nevertheless, as indicated in Table 6, our algorithm's F1 score remains largely unaffected. For \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Data Type**} & \multicolumn{3}{c}{**Storage (MB)**} & \multirow{2}{*}{\
\begin{tabular}{c} **Runtime** \\ **Memory** \\ **(MB)** \\ \end{tabular} } \\ \cline{2-2} \cline{6-9}  & **Input** & **Output** & **Input** & **Data** & **Annotation** & **Total** & **(MB)** & **Runtime** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} 3D Point \\ Cloud-based [19] \\ \end{tabular} } & \multirow{3}{*}{3D Point Cloud} & \multirow{3}{*}{3D Annotation} & \multirow{3}{*}{14.16} & \multirow{3}{*}{14.16} & \multirow{3}{*}{3.10} & \multirow{3}{*}{17.26} & \multirow{3}{*}{12.36} & \multirow{3}{*}{243.38} & \multirow{3}{*}{0.16} \\  & & & & & & & & \\ \cline{1-1} \cline{5-10}  & \multirow{3}{*}{3D Point Cloud} & \multirow{3}{*}{3D Annotation} & \multirow{3}{*}{14.16} & \multirow{3}{*}{14.16} & \multirow{3}{*}{3.10} & \multirow{3}{*}{17.26} & \multirow{3}{*}{0.03} & \multirow{3}{*}{6.38} & \multirow{3}{*}{223.40} & \multirow{3}{*}{2.95} \\  & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of storage usage between the comparison algorithm and the proposed algorithm. further algorithm optimization, we propose to explore incorporating an elevation-detection step based on Lidar's three-dimensional data in our approach in the future. Alternatively, introducing a three-dimensional probability grid map could evaluate obstacle pitch angles using vehicle chassis height as a constraint.