# A Quantitative Evaluation of UAV Flight Parameters for SfM-Based 3D Reconstruction of Buildings
## 4 Validation
### Single Shooting Pattern
#### 4.1.5 Response Surface Methodology (RSM)  
RSM approximates the relationship between selected independent variable pairs and the dependent variable using a quadratic polynomial regression model and presents the results as a visual response surface or contour plot. This technique is useful for intuitively identifying patterns of relationships between variables and local regions of optimal variable combinations that optimize specific outcome metrics. Therefore, to explore the combined effects of two shooting variables changing simultaneously on specific SfM outcome metrics and potential interactions beyond the influence of individual variables, this study employed RSM (Table 8).  
Figure 4: PCA K-means scatter plot and cluster.  
For the analysis, a quadratic polynomial regression model was constructed for five predefined combinations of (independent variable pairs \(\times\) dependent variable), and the explanatory power (Adjusted R2) of each model varied from approximately 0.42 to 0.80 depending on the analyzed combination, confirming that the model's suitability varies depending on the case. For example, in the Circular pattern, the model predicting Reprojection Error using Radian and Tilt angle as variables showed an adjusted R2 value of approximately 0.80, indicating relatively high explanatory power and suggesting that the quadratic relationship between the variable combination and the result indicator is well explained.  
The prediction results of each RSM model were visualized as contour plots showing the trend of changes in the predicted values of the dependent variable according to changes in the two independent variables. The analysis of the Circular pattern showed that Final Points increased as both offset and Tilt angle increased, with the contour lines forming a gentle ridge shape where the influence of Tilt angle appeared to be greater (Figure 5). The optimal region that maximizes the number of points in this model is interpreted as being in the upper right of the plot, i.e., the region where both variables are high. On the other hand, Reprojection Error exhibited a distinct elliptical valley-shaped response surface, minimizing when both Radian and Tilt angle were within specific ranges (as described in the text, Radian \(\approx\) 10-15 m, Tilt \(\approx\) 55-65\({}^{\circ}\)). When the optimal region is exceeded, the reprojection error increases, and a tendency for the error to increase more prominently as the shooting radius increases was observed.  
The results of the surface pattern analysis showed a different pattern (Figure 6). Computation Time increased linearly as Forward overlap and Side overlap decreased (i.e., as the overlapping area between images increased), and the contour lines appeared as straight lines that were almost parallel. Final Points depended mainly on Forward overlap, increasing sharply as this value decreased (i.e., as the overlap increased), while the influence of Tilt angle was negligible, with contour lines appearing almost vertical. Similarly, Reconstruction Completeness also primarily depends on Side overlap, showing an increasing trend as the overlap increases, while the influence of Tilt angle is negligible, resulting in contour lines that are nearly vertical.