## 2 Materials and Methods
### Detection Precision  
When evaluating classification results, it is common practice to use the True Positive (TP), False Positive (FP), False Negative (FN), and True Negative (TN) to describe the relationship between the predicted and actual results, as shown in Table 4.  
Loop detection is a classification task, and commonly used evaluation metrics include precision and recall. Precision represents the proportion of correctly predicted positive samples out of all samples predicted as positive, while recall indicates the proportion of correctly predicted positive samples out of all actual positive samples. By using these two metrics, we can obtain a more comprehensive understanding of the different aspects of the performance of the loop detection method. The formulas for these metrics are provided in (22) and (23). \[Precision=\frac{TP}{TP+FP} \tag{22}\]  
\[Recall=\frac{TP}{TP+FN} \tag{23}\]  
Since the publicly available datasets do not provide ground truth for loop-closure frames, we used an automated tool to obtain the ground truth for this experiment. Figure 7 below shows a schematic of the KITTI experimental trajectory, with the red trajectory indicating the acquired loop-closure ground truth. To enhance the diversity of the experiment, we also included a local dataset collected in an underground parking lot. The data comprise \begin{table}
\begin{tabular}{c c c} \hline \hline
**Results/Fact** & **True** & **False** \\ \hline
**True** & True positive (TP) & False positive (FP) \\
**False** & False negative (FN) & True negative (TN) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relationship between classification results and fact. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **Sequences** & **00** & **05** & **06** & **07** \\ \hline \multirow{3}{*}{Max} & BOW2 & 13.70 & 9.35 & 3.70 & 6.51 \\  & Proposed method & 8.69 & 5.32 & 2.38 & 2.16 \\  & Reduction & 36.6\% & 43.1\% & 35.7\% & 66.8\% \\ \hline \multirow{3}{*}{Mean} & BOW2 & 5.51 & 4.13 & 2.95 & 3.04 \\  & proposed method & 4.35 & 2.52 & 1.05 & 1.04 \\  & Reduction & 21.0\% & 43.8\% & 64.4\% & 65.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of running time (max and mean in _ms_) between the proposed method and BOW2. The sequences are from the KITTI dataset. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **Sequences** & **Gattaca-1** & **Gattaca-2** & **Parking-1** & **Parking-2** \\ \hline \multirow{3}{*}{Max} & BOW2 & 6.47 & 17.03 & 6.03 & 7.16 \\  & Proposed method & 3.64 & 11.36 & 6.01 & 6.07 \\  & Reduction & 43.7\% & 33.3\% & 0.2\% & 15.2\% \\ \hline \multirow{3}{*}{Mean} & BOW2 & 3.13 & 5.72 & 3.26 & 3.50 \\  & Proposed method & 1.85 & 5.36 & 1.71 & 2.01 \\  & Reduction & 40.9\% & 6.3\% & 47.5\% & 42.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of running time (max and mean in _ms_) between the proposed method and BOW2. The sequences are from the UMA dataset. around-view images primarily used for automated parking functions. The experimental trajectory and loop-closure ground truth are shown in Figure 8, with the red trajectory representing the loop-closure ground truth. Precision and recall are mutually exclusive metrics, with the ideal scenario being high recall and high precision. An important metric for evaluating detection performance is the precision-recall curve. The methods selected for comparison are BOW2 and SRLCD [39]. [PERSON] et al. [39] proposed an intriguing loop-detection method, SRLCD, which differs from feature-based methods, like BOW2. Their research suggests that salient regions in images serve as excellent descriptors, aligning with human recognition processes. Moreover, their method matches salient regions in the frequency domain, providing rotation and scale invariance. We tested the proposed method and the comparison methods based on the 00 sequence from the KITTI dataset, which is lengthy and rich in loop-closure scenes, and plotted the precision-recall curves.