# A Quantitative Evaluation of UAV Flight Parameters for SfM-Based 3D Reconstruction of Buildings
## 4 Validation
### Analysis of Multiple Shooting Patterns
#### 4.2.2 Pareto Optimization of Multiple Shooting Patterns  
The TOPSIS analysis comprehensively considered multiple performance criteria with equal weights to rank the overall efficiency of composite shooting patterns. This confirmed that combinations such as C_O40_L_O30 are excellent strategies that satisfy multiple criteria in a balanced manner. However, certain objectives (e.g., fast processing time or highest accuracy) may be more important than others. Therefore, in addition to the overall ranking from TOPSIS, it is important to identify which composite shooting strategies are the most efficient alternatives for performance goal pairs with significant trade-offs (e.g., time vs. error). To this end, we performed a Pareto optimization analysis on the composite shooting pattern data, similarly to the single pattern analysis, to identify the Pareto frontier.  
The analysis was conducted using composite pattern data targeting the same key goal combinations considered in the single pattern analysis, and the sets of Pareto optimal solutions and frontier forms for each combination are shown below (Figure 8). The analysis results show that different composite shooting pattern combinations form a Pareto optimal frontier for each goal combination, indicating an efficient trade-off between the goals. As a specific example, only three composite pattern combinations were identified as Pareto optimal solutions for the 'Time_vs_Error' objective combination. These combinations are located in the efficient region in the lower left corner of the visualization results, achieving relatively short computation times (estimated to be in the range of 0-35 min) and low reprojection errors (approximately 1.08-1.09) simultaneously. Additionally, for the 'Time_vs_Points' combination, a total of 13 composite pattern combinations formed the Pareto frontier. This frontier exhibited a convex upward trend from the lower left (short time, few points) to the upper right (long time, many points), indicating that the initial time investment (estimated to be in the range of 0-70 min) is highly effective for increasing the number of points, but the efficiency of additional time investment decreases sharply thereafter, demonstrating the 'diminishing returns' trend in composite pattern analysis. Similar Pareto optimal sets were identified for other key goal combinations such as 'Error_vs_Points' and 'Time_vs_Completeness', with each frontier presenting the most efficient trade-offs between the respective goals.  
In conclusion, even when using composite shooting patterns, non-dominated strategies exist that demonstrate superior or at least equivalent efficiency compared to other combination strategies under specific performance goal combinations. Therefore, when selecting the final composite shooting strategy, it is reasonable to prioritize the comprehensive performance rankings derived from the TOPSIS analysis (Table 10) while selecting the solution that provides the most appropriate balance on the Pareto frontier (Figure 7) for the relevant goal combinations based on the specific requirements of the project (e.g., time constraints, quality goals).