## 3 Results
### Image Registration Model  
The image alignment results were evaluated by comparing the model performance parameters of the three selected methods (CB, FT, and RG). The coefficient of determination (R2) and root mean square error (RMSE) were chosen as the main indicators to assess the fitting of the model as they provided an overall view of the goodness of fit and an average accuracy of the interpolation. The accuracy of the spatial alignment between images was assessed by measuring the remaining residual displacement among the multispectral bands after fitting the model. This was expressed as the residual offset error along the x-axis (Xerr) and y-axis (Yerr) expressed in pixels. Figure 4 shows the results of the interpolation of the model applied to the experimental data, considering the offsets of the B, G, NR, and RE bands to the R band. The offsets were analyzed along both the X- and Y-axes and considering all five positions, using the CB, FT, and RG methods. The adjusted R2 indicated that all models achieved a very high degree of correlation with the experimental data. Similarly, the residual offset error along the x and y axes was, on average, between \(\pm\)2 and \(\pm\)3 pixels. Furthermore, the comparison highlighted that the experimental methods proposed in previous work [24] demonstrated good performance in offset calculation, showing no significant differences compared with the conventional RG method. Figure 4: Results of the model interpolation on the experimental data, with the offsets of the B, G, NR, and RE bands relative to the R band, analyzed along the X-axis and Y-axis using the CB, FT, and RG methods. The B and NR bands exhibited the best overall results for both axes, indicating a good fit for the model. Specifically, Tables 3-5 show that the offsets of the B vs. R band demonstrated a high correlation (mean adjusted R\({}^{2}\): 0.9986 and 0.9835 on the x and y axes, respectively) and low errors (mean RMSE: 1.0529 and 1.3834 on the x and y axes, respectively). This same trend was confirmed by the results of the NR band offsets, showing mean adjusted R\({}^{2}\) of 0.9916 and mean RMSE of 1.2636 along the x-axis and mean adjusted R\({}^{2}\) of 0.9923 and mean RMSE of 1.2803 along the y-axis. In contrast, the G band, compared with the R band, exhibited the worst correlation results along the x-axis, as evidenced by an R\({}^{2}\) value of \(-\)0.0159. Similarly, the RE band showed fitting issues along the y-axis with mean adjusted R\({}^{2}\) values of \(-\)0.2168. The coefficients of the model, a and b, exhibited variability both across the bands and along the axes. In particular, the wide 95% confidence intervals for the \(b\) coefficient along the \(x\) and \(y\) axes for the G and RE bands confirmed the poor performance of the model for these two bands. Nevertheless, the obtained model reasonably explained the effect of the \(x\) distance on the \(y\) geometric offset, highlighting an inverse proportionality between \(x\) and \(y\), compensated by the value of \(b\). Example calculations are summarized in Table 6, which presents the reference values of the Y offset model for the B vs. R band of the CB method (\(a=-5.597\), \(b=28.970\)) found in Table  
defined by a. However, as the distance decreased, the relative error increased, suggesting that the model must necessarily be robust. Unlike the interpolating model presented in [24], which had no direct physical interpretation, the proposed inverse linear model provided a clearer comprehension of the dependence of geometric offset on sensor distance. This physical interpretation was particularly important for applications requiring high alignment accuracy, as confirmed by the error values reported in Table 6. The ability to describe the trend of offsets as a function of distance through an analytical relationship improved the applicability of the model, offering a more interpretable and generalizable solution than previous approaches.