## 3 Results  
In this study, we conducted a comparative analysis between the proposed overlapping image-set determination methodology and NoM- and BoVW-based approaches using four target images selected from two datasets. The evaluation of the results of the image set from each method was based on accuracy and processing time. In addition, we compared and analyzed the accuracy of the bundle adjustment results using an image set. Specifically, we examined the precision, average overlap area ratio, and the correlation between similarity and overlap from the perspective of overlapping image set selection accuracy, followed by a comparison of processing times. In addition, we investigated the precision of the bundle adjustment results and the reprojection error to further evaluate the performance of the methods. The accuracy of the overlapping image set selection, evaluated based on precision, average overlap area ratio, and the correlation between similarity and overlap, appeared to be relatively higher in the proposed methodology and the NoM-based approach than in the BoVW-based approach (Table 5). Specifically, both the proposed methodology and the NoM-based approach exhibited an average precision of 96%, whereas the BoVW-based approach showed a lower precision of 62%. In particular, for Targets 3 and 4, the proposed methodology and NoM-based approach demonstrated 100% precision each, whereas the BoVW-based approach exhibited precisions of 60% and 50%, respectively. This indicates that the image sets selected from the proposed methodology and NoM for Targets 3 and 4 were correctly composed of genuinely overlapping images, whereas 40% and 50% of the image sets selected from BoVW consisted of incorrectly selected non-overlapping images. This discrepancy may be attributed to the lack of diversity in the BoVW codebook, especially in datasets like Dataset 2, where Targets 3 and 4 were chosen. This is because Dataset 2 consists of uniform textures, leading to a lack of diversity in the BoVW codebook and resulting in a relatively lower accuracy. The average overlap area ratio was the highest in the following order: the NoM-based method, proposed method, and BoVW-based method, with average values of 0.57, 0.55, and 0.40, respectively (Table 6). Figures 9-11 illustrate the actual overlapping areas of the image set selected for Target 2. In these figures, non-overlapping images are delineated with a red border, whereas overlapping images are demarcated with a yellow border, indicating their respective overlapping areas. Both the proposed method (Figure 9) and the NoM-based approach (Figure 10) yielded an average overlap area ratio of 0.53, suggesting \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Target**} & \multicolumn{3}{c}{**Precision (\%)**} \\ \cline{2-4}  & **NoM** & **BoVW** & **Proposed** \\ \hline
1 & 94 & 83 & 94 \\
2 & 89 & 56 & 89 \\
3 & 100 & 60 & 100 \\
4 & 100 & 50 & 100 \\ Average & 96 & 62 & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of precision among proposed method, NoM, and BoVW-based approaches. that more than half of the images constituting the image set overlapped by more than 50% with Target 2. By contrast, the BoVW-based approach (Figure 11) demonstrated an average overlap area ratio of 0.40, signifying a relatively low overlap ratio between the images forming an image set. Consequently, it can be inferred that the proposed method and NoM-based approach generate an image set with a significantly higher overlap ratio than the BoVW-based approach. Finally, the correlation between similarity and overlap was the highest in the following order: the proposed methodology, NoM-based approach, and BoVW-based approach. The proposed methodology and the NoM-based approach exhibited average correlations of 0.88 and 0.84, respectively, while BoVW showed a relatively lower correlation of 0.53 (Table 7). In particular, for Target 4, the correlation of the proposed methodology was very high at 0.97, whereas that of the BoVW-based approach was low at 0.21.