## 2 Results and Discussion
### Influence of ground sampling distance  
The influence of the DSM's ground sampling distance is one of the factors that influence the quality of the generated models. A recent study involving SPOT-HRV and Terra ASTER data [30] described the best resolution as twice the satellite's image pixel size to avoid degradation of the DSM's structure (i.e., 20 m for SPOT-HRV and 30 m for Terra ASTER).  
When evaluating the multi-resolution DSMs generated at the desired resolution directly from the Cartosat-1 images in the range of 5 - 20 m, for Mausanne les Alpilles we observed a RMSE between 7.1 m and 9.4 m, while for Salon de Provence we obtained a RMSE between 4.5 m and 5.1 m. Whenanalyzing results in the range of 25 - 85 m resolution, for Mausanne les Alpilles we observed a RMSE between 7.9 m and 12.4 m, while for Salon de Provence we obtained a RMSE between 5.0 m and 11.7 m with respect to the high-resolution reference DSM and a RMSE between 7.1 m and 14.7 m with respect to MNT DBTOPO(r) DTM. When analyzing results at the SRTM90 resolution (90 m), for Mausanne les Alpilles we obtained a RMSE of 7.1 m, while for Salon de Provence a RMSEs of 10.3 m and 15.3 m, respectively comparing to the high-resolution reference DSM and MNT DBTOPO(r) DTM.  
When evaluating the multi-resolution DSMs generated by downsampling higher-resolution models previously generated (5 m) we obtained a remarkable improvement for both the test sites (Figures 1 and 2) and the DSMs' accuracy did not depend neither upon the ground sampling distance nor upon the terrain's slope and was almost constant. The overall accuracy for all the multi-resolution DSMs showed a RMSE between 6.8 m and 7.1 m for Mausanne les Alpilles and a RMSE between 4.3 m and 4.4 m for Salon de Provence (Figures 3 and 4). A more surprising improvement was achieved when comparing the multi-resolution Cartosat-1 DSMs with Reference 3D(r) specifications. In this case Reference 3D(r) requirements were always met, regardless the DSM's resolution and the terrain's slope (Tables 1 and 2). As a drawback, this method is disadvantageous in terms of computation time and resources since a higher-resolution DSM must be computed to produce a lower-resolution terrain model.  
Figure 3: Summary of results for the Cartosat-1 multi-resolution DSMs generated over Mausanne les Alpilles test site. Comparison with respect to the high-resolution reference DSM (reference DSM-Cartosat-1 DSM): (a) for DSMs generated at the desired resolution directly from the Cartosat-1 images; (b) for DSMs generated by downsampling the 5m resolution Cartosat-1 DSM. All values refer to a comparison over the whole test site.  
Figure 2: Residuals for the 10 m resolution DSM generated over Salon de Provence (France).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Resolution** & \multicolumn{3}{c}{**LE90 (m) vs. slope \({}^{\text{(a)}}\)**} & \multicolumn{3}{c}{**LE90 (m) vs. slope \({}^{\text{(b)}}\)**} \\
**(m)** & \(<20\%\) & \(20\%-40\%\) & \(>40\%\) & \(<20\%\) & \(20\%-40\%\) & \(>40\%\) \\ \hline  
\hline \end{tabular}
\end{table}
Table 1: Summary of residuals vs. slope for Cartosat-1 DSMs generated over Mausanne les Alpilles test site. (a) for DSMs generated at the desired resolution directly from the Cartosat-1 images. (b) for DSMs generated by downsampling the 5m resolution Cartosat-1 DSM. All values refer to a comparison over the whole test site.  
Figure 4: Summary of results for the Cartosat-1 multi-resolution DSMs generated over Salon de Provence test site. Comparison with respect to the high-resolution reference DSM (reference DSM-Cartosat-1 DSM): (a) for DSMs generated at the desired resolution directly from the Cartosat-1 images; (b) for DSMs generated by downsampling the 5m resolution Cartosat-1 DSM. All values refer to a comparison over the whole test site.