## 4 Experiments
### Image-Based Monte Carlo Localization  
To verify the robustness of our topological navigation method, we performed the experiment on the topological map shown in Figure 7. In image-based Monte Carlo localization, a series of similarities between the currently view image and the keyframe images in topological nodes generated by image retrieval are adopted to compute the importance weights of the possible location of the robot. Generally speaking, the higher the ranking of the retrieved image, and the more similar to the query image, the greater the weight of the samples assigned to that location. For an indoor mobile robot, the similarity between two images decreases as the captured distance increases. In an actual navigation experiment, in order to judge whether the robot reaches a certain target position, we steered the robot to collect a series of image in different indoor environments and randomly select frames to analyze the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**MAP**} & \multicolumn{2}{c}{**Times(s)**} \\ \hline  & **Oxford 5k** & **Pair 6k** & **Oxford 5k** & **Pair 6k** \\ \hline [PERSON] et al. Reference [43] & 56.0 & – & – & – \\ [PERSON] et al. Reference [44] & 65.7 & – & – & – \\ [PERSON] et al. Reference [45] & 77.3 & 86.5 & 2.9 & 3.52 \\ [PERSON] et al. Reference [29] & 78.6 & 84.2 & 1.08 & 1.36 \\ Ours & 78.1 & 83.8 & 0.17 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison with existing methods. Figure 8: Examples of the proposed image retrieval method. The first column is the query image with blue contour, and the others with green contour are retrieved images. relationship between the similarity and spatial distance of two images. In this way, the approximate distribution of the captured distance under a certain degree of similarity can be obtained through experimental statistics. The result is shown in Figure 9. As can be seen, the captured distance between two images is within 1 m when the similarity is greater than 0.9 and the captured distance between two images is within 0.5 m when the similarity is greater than 0.85. Therefore, we set the threshold of similarity to 0.85 in this experiment, which means that we judged the robot to reach the target position when the similarity between the currently view image and the keyframes in target nodes was greater than 0.85. In this section, to quantitatively evaluate the performance of localization, comparative experiments among the proposed image-based Monte Carlo localization method and a well-known metric-based localization method [46] were performed, as shown in Figure 10. The metric-based navigation method which adopts a particle set of fixed size to simulate the posterior probability is performed by providing the specific geometric coordinates. Figure 10a depicts the number of samples versus execution step of the two localization method. Figure 10b shows the CDF of the localization error versus execution step of two localization methods. It can be seen that the performance of our image-based localization method obviously outperforms metric-based method in terms of localization accuracy. The localization error of the proposed localization method converges rapidly after a short period of fluctuation. Such fluctuation of localization error generally occur in the initial stage of global localization, which is mainly due to the incorrect matching of image-to-node in topological localization, namely perceptual aliasing. But the coarse-to-fine mechanism in our image-based Monte Carlo localization provides the robot with the capability to restore from the perceptual aliasing and converge to the real location rapidly. Additionally, as depicted in Figure 10, the proposed visual localization method is overall robust, and the average localization error is less than 50 cm when the localization process is stable after a few iterations, which is enough to meet the requirements for global localization.