## 2 Proposed Methodology
### Hybrid BoVW-NoM Technique
In the fourth stage, the sizes of the candidate and image sets are determined based on the characteristics of each target image. This approach addresses the variability in the number of overlapping images depending on the capture path of the target image. To achieve this, we utilized the adaptive threshold determination method proposed by [PERSON] and [PERSON] (2020) [31]. This method leverages the fact that overlapping images have higher similarity scores than non-overlapping images and calculates similarity thresholds using statistical estimates of the similarity scores. To improve the accuracy of the image set, we deliberately selected a greater number of candidate images than the final set size. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Image Scale** & **Original** & **50\%** & **25\%** & **10\%** \\ \hline Down-sampling & 0 & 120 & 97 & 91 \\ Codebook generation & 4031 & 1385 & 562 & 93 \\ Image-set determination & 5546 & 973 & 170 & 70 \\ Total & 9578 & 2478 & 829 & 253 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Efficiency comparison of image scales (seconds). Figure 6: Utilization of extracted features in codebook generation and image matching. This approach ensures the inclusion of clearly overlapping images, which is essential for precise image location estimation [28]. The expanded candidate pool compensates for potential limitations in the BoVW codebook generation process, where visually similar but non-overlapping images might receive high similarity scores. Figure 7a,b illustrates the application of this threshold determination method to Targets 1 and 2, respectively. The thresholds for both candidate and image set sizes were dynamically determined based on the characteristics of the targets and the distribution of similarity scores. Once the candidate size was established, images were selected based on their similarity scores and sorted in descending order. This approach effectively balances the need for comprehensive image sets while avoiding the inclusion of non-overlapping images, thereby optimizing the subsequent image localization process. In the final stage of the proposed method, the candidate images were matched with the target image based on NoM to determine the overlapping image set. This method utilizes features directly extracted from images for matching, assuming that images with many matched features exhibit high similarity and overlap. To enhance efficiency, the features extracted in the previous stage were reused for matching. The image set was selected from the candidates based on a predetermined number of images, prioritizing images with a high number of matched features. Figure 8a,b depicts the candidate images based on the BoVW codebook for Target 4 and the final selected image set using NoM. Images with yellow borders represent images overlapping with the target image, whereas those with red borders do not overlap. Although candidate selection based solely on a BoVW-based image search may include many non-overlapping images, the results of feature matching effectively exclude non-overlapping images. Consequently, even overlapping images with low similarity during candidate exploration can be correctly matched through the feature-matching process and selected as results. Figure 8: Visualization of candidate selection and final image-set determination for Target 4: (**a**) BoVW-based candidates; (**b**) final image-set determination using NoM (red borders: images that do not overlap, yellow borders: images that overlap with the target image). Figure 7: Threshold determination method for candidate and image set: (**a**) Target 1; (**b**) Target 3.