## 2 Proposed Methodology
### Evaluation Method  
In this study, the performance of the proposed methodology was validated by comparing and analyzing the results of the BoVW- and NoM-based approaches with those of the proposed methodology. The performance was evaluated based on the results of deriving overlapping image sets and performing bundle adjustments using the derived overlapping image sets. The evaluation was conducted using selected target images as references. Specifically, the similarity was assessed between the four selected target images and the entire corresponding dataset. Based on this assessment, bundle adjustment was performed for the four resulting overlapping image sets to evaluate the performance of the methodologies. The final image set size determined by the thresholds of the proposed methodology was applied to the BoVW and NoM methods to ensure that the final overlapping image set of each method maintained the same number of images. The specific details of each evaluation item are presented in Table 4.  
The performance of the proposed method was evaluated in comparison with NoM- and BoVW-based approaches, focusing on both accuracy and computational efficiency. Methodologies that exhibit faster processing speeds while maintaining accuracy are considered superior in terms of performance. To quantify the accuracy of the overlapping image set results, three key metrics were employed. 1. Precision of Overlap: This metric measures the ratio of images in the set that genuinely overlap with the target image. True negatives are not considered in this calculation, as precision is prioritized over recall in image localization accuracy [28]. 2. Average Overlap Area Ratio: This metric evaluates whether an image set consists of images with relatively high overlap, calculated as the mean ratio of overlap between the target image and the images in the set. Unlike precision, which assesses the presence of overlap, the average overlap area ratio measures the degree of overlap. An image set composed of images with a higher overlap tends to form more robust image networks, which is advantageous for precise bundle adjustment. 3. Correlation between Similarity and Overlap: This metric assesses the relationship between the similarity scores of images in the set and their actual overlap with the target image. A strong correlation indicates that the similarity scores accurately reflect the overlap ratio, enabling more effective thresholding and image selection. Consequently, a high correlation enables fine-tuning of thresholds to prevent the exclusion of images with high actual overlap but unexpectedly low similarity scores from the image set. The evaluation of bundle adjustment results using an image set involves assessing the precision of exterior orientation parameters (EOP) and root mean square (RMS) residuals \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Name** & **Description** \\ \hline \multirow{4}{*}{Image set determination} & \multirow{2}{*}{Precision} & \multirow{2}{*}{Proportion of overlapping images relative to the total} \\  & & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & & \\ \hline \multirow{4}{*}{Bundle adjustment} & \multirow{2}{*}{Precision} & \multirow{2}{*}{Mean standard deviation of EOP} \\  & & & \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance evaluation metrics for image-set determination and bundle adjustment. for the image coordinates. Bundle adjustment was performed individually for each target image and the corresponding set. Because it was assumed that some GNSS information might be missing, only half of the available GNSS information from the images was used. The number and arrangement of ground control points (GCPs) vary depending on the image set included. Therefore, GCPs were not utilized to evaluate the impact of the image set obtained from the proposed methodology on bundle adjustment. Furthermore, images that could potentially compromise the stability or accuracy of bundle adjustment owing to localization failures were also excluded.