## 4 Experimental Results
### General Performance  
We evaluated the performance of our loop closure detection approach on four KITTI datasets with loop closures: KITTI 00, KITTI 05, KITTI 06, and KITTI 07. Table 2 presents the precision and recall of our proposed approach for the final configuration on the aforementioned sequences. If the accuracy of loop closure detection is low, it indicates a significant number of incorrect results being identified as loop closure occurrences. Constructing loop closure constraints based on these incorrect results can further deviate the optimized  
Figure 6: The feature extraction result of different \(\epsilon_{c}\) and \(\epsilon_{r}\) settings on the image shown in Figure 5, where each local region feature is indicated by a different color. Figure 7: Two sets of matching images result in the KITTI07 dataset, where each local region feature is indicated by a different color, and the matching features are connected by a line. The top result is the correct match while the bottom one is incorrect. motion trajectory. Conversely, a low recall rate in loop closure detection leads to the omission of many correct loop closure instances, resulting in the loss of valuable loop closure constraint information. This, in turn, may prevent the correction of the motion trajectory or weaken the effectiveness of the corrections made. The proposed method achieved high accuracy and recall rates in all four sequences, with only a few false positives observed in two of them. Following the completion of loop closure detection, additional loop closure verification can be employed to eliminate false matching results and improve accuracy. A high recall rate ensures successful detection of nearly all loop closure locations and the construction of corresponding loop closure constraints. At the same time, a high accuracy rate ensures that no false matching loop closure results adversely affect the estimation of the motion trajectory. Figure 8 shows the evolution of the vocabulary size for these four sequences. The traditional BoW model typically uses feature points to construct a vocabulary tree, where dozens or even hundreds of feature points can be extracted from an image. This type of BoW model constructs the vocabulary tree from training sets during the offline stage. To ensure adaptability to complex and changable environments, the vocabulary size should not be too small. Consequently, these constraints result in vocabulary sizes reaching \(1\times 10^{5}\). For instance, the FAB-MAP 2.0 algorithm employs a vocabulary tree consisting of up to 100,000 words. Similarly, the iBoW-LCD algorithm performs online vocabulary tree construction on a large-scale sequence such as KITTI 00, which includes up to 4000 images, resulting in a final vocabulary tree containing over 800,000 words. However, our proposed approach demonstrates significantly smaller vocabulary sizes, even when applied to KITTI 00, the number of words remains below 1200, which differs by two orders of magnitude compared to traditional methods' vocabulary sizes. This reduction in vocabulary size greatly enhances the computational efficiency of the loop closure detection algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Image** & **Precision (\%)** & **Recall (\%)** \\ \hline KITTI 00 & 4007 & 93.52 & 76.53 \\ KITTI 05 & 2135 & 92.49 & 74.76 \\ KITTI 06 & 995 & 100 & 77.64 \\ KITTI 07 & 756 & 100 & 66.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Precision and recall of our proposed approach for the final configuration. Figure 8: The evolution of the vocabulary size for these four sequences. Figure 9 illustrates the response time of our proposed approach per image for these four sequences. It can be observed that, for time indices before 400, the response time remains consistently below 0.3 ms. This can be attributed to the small vocabulary size, resulting in a relatively small amount of data to process during vocabulary tree updates and image retrieval.