## 4 Conclusions  
In this study, we propose an enhanced method for determining overlapping image sets to improve the accuracy and efficiency of image localization. Our approach integrates the NoM-based approach, which is known for its relatively high accuracy but low efficiency, with the BoVW-based method, which exhibits a relatively faster processing speed but lower accuracy. This method sequentially applies image-similarity searches based on BoVW and NoM to construct overlapping image sets. The method involved the following steps. First, we applied down-sampling to the input images to improve the efficiency of the overall process. We then extracted feature points using the SURF algorithm and conducted a BoVW-based image search using these feature points. Based on the BoVW-based image similarity, we determined the size of the candidate and image sets, and selected candidates accordingly. Finally, we determined the image sets by evaluating the similarity of the images based on the NoMs for the selected candidates. The proposed method demonstrated improved performance compared with both NoM- and BoVW-based approaches. A comparative analysis of the four target images revealed that the proposed method demonstrated a higher accuracy than the BoVW-based approach, while also achieving faster processing speeds than the NoM-based approach. The average precision of the proposed method remained consistent with that of the NoM-based approach at 96%, surpassing that of the BoVW-based approach by 62%. Additionally, metrics such as the overlap area ratio and the correlation between similarity and overlap showed higher values for the proposed method, averaging 0.55 and 0.88, respectively, compared to 0.40 and 0.53 for the BoVW-based approach. Furthermore, the processing time of the proposed method was approximately 0.11 times shorter than that of the NoM-based approach, achieving a similar level of accuracy at a faster pace. Moreover, in the bundle-adjustment results using the derived image set, the proposed method exhibited \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Mean Standard Deviation of EOPs (Precision)**} & \multicolumn{3}{c}{**Reprojection**} & \multicolumn{3}{c}{**Bundle Adjustment**} \\  & **Target** & **X0** & **Y0** & **Z0** & **\(\omega\)** & **\(\varphi\)** & **\(\kappa\)** & **RMS Residual** & **Number of** & **Number of** \\  & & **(m)** & **(m)** & **(m)** & **(degree)** & **(degree)** & **(degree)** & **(pixel)** & **Successful** & **Excluded** \\  & & & & & & & & & & & \\ \hline \multirow{3}{*}{1} & NoM & 0.088 & 0.075 & 0.013 & 0.042 & 0.041 & 0.076 & 0.66 & 18 & 1 \\  & BoVW & 0.092 & 0.091 & 0.201 & 0.372 & 0.339 & 0.100 & 1.11 & 16 & 3 \\  & Proposed & 0.004 & 0.004 & 0.001 & 0.003 & 0.004 & 0.006 & 0.55 & 18 & 1 \\ \hline \multirow{3}{*}{2} & NoM & 0.053 & 0.067 & 0.037 & 0.443 & 0.391 & 0.086 & 0.43 & 16 & 2 \\  & BoVW & 0.292 & 0.494 & 0.062 & 0.729 & 1.190 & 0.212 & 0.90 & 18 & 0 \\  & Proposed & 0.056 & 0.069 & 0.036 & 0.456 & 0.403 & 0.101 & 0.52 & 16 & 2 \\ \hline \multirow{3}{*}{3} & NoM & 0.030 & 0.019 & 0.026 & 0.075 & 0.091 & 0.010 & 0.43 & 11 & 0 \\  & BoVW & 0.147 & 0.169 & 0.174 & 0.784 & 0.800 & 0.231 & 0.90 & 7 & 4 \\  & Proposed & 0.044 & 0.025 & 0.123 & 0.057 & 0.068 & 0.058 & 0.52 & 11 & 0 \\ \hline \multirow{3}{*}{4} & NoM & 0.129 & 0.103 & 0.100 & 0.307 & 0.336 & 0.055 & 1.10 & 19 & 0 \\  & BoVW & 0.271 & 0.246 & 0.175 & 0.623 & 0.441 & 0.246 & 1.81 & (2 block) & 2 \\ \cline{1-1}  & Proposed & 0.149 & 0.114 & 0.090 & 0.229 & 0.326 & 0.073 & 0.99 & 19 & 0 \\ \hline \multirow{3}{*}{Mean} & NoM & 0.075 & 0.066 & 0.044 & 0.217 & 0.215 & 0.057 & 0.830 & 16 & 0.75 \\ \cline{1-1}  & BoVW & 0.201 & 0.250 & 0.153 & 0.627 & 0.693 & 0.197 & 1.558 & 14.5 & 2.25 \\ \cline{1-1}  & Proposed & 0.063 & 0.053 & 0.063 & 0.186 & 0.200 & 0.060 & 0.750 & 16 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Bundle adjustment results for image set constructed by proposed method, NoM, and BoVW-based approaches.