## 3 Experimental Section
### Methods
Although the computational power of the modern computers is impressively increasing [36], the calculation of high-resolution DSMs for large territories using ordinary workstations is still limited by system resources, therefore, from an operational point of view, the data processing must be optimized. As metadata we used the predetermined RPCs supplied by ISRO along with sixty tie points automatically extracted with a regular grid scheme. Under these conditions, the y-parallax of the quasi-epipolar images was 1.27 pixel (corresponding to 3.18 m on the ground). Any improvement in the DSMs' accuracy was observed using more tie points. The image matching was done using a moving window size of 30 pixels and a minimum correlation coefficient of 0.80 and data processing was stopped just before the highest pyramid level (at full resolution): this led to a reduction of the computing time by a factor of 4.6 (size of images four times smaller) without sensible degradation in the DSMs. For geocoding, we investigated how the GCPs' number and geometric distribution influenced the product's accuracy, while the influence of GCPs' accuracy on the produced DSMs was not tested because the dataset supplied within C-SAP never allowed such validation. Finally, we verified that the DSM's generation process may be enhanced by applying a simple moving average low-pass filter with optimized kernel size (\(7\times 7\) pixels). Dozens of DSMs were generated for resolution ranging from 5 m to 90 m and their vertical accuracy has been manually evaluated with respect to the terrain's characteristics and sampling interval. Regarding the generation process we used two different approaches: first we generated DSMs at the desired resolution directly from the Cartosat-1 images (here resampling was performed as a part of the data processing) and then we generated DSMs by downsampling the 5 m resolution Cartosat-1 DSMs previously generated. The main difference of the two methods concerns how filtering was applied. In the first case, filtering was applied to the downsampled data, thus involved a ground surface depending on the DSM's resolution. In the second case, filtering was always applied to the higher-resolution DSM (5 m), and then downsampling was performed. Results were evaluated with respect to the following reference data:  
* A set of ICPs extracted from the original C-SAP dataset (ranging from to 23 to 31 for Mausanne les Alpilles and from 13 to 21 for Salon de Provence). The vertical accuracy of reference ICPs was the same of source dataset (0.05 m for Mausanne les Alpilles and better than 2.5 m for Salon de Provence);
* The high-resolution reference DSM resampled to the Cartosat-1 DSM's resolution;
* The medium-resolution reference DTM resampled to the Cartosat-1 DSM's resolution (used for comparison at resolution exceeding 25 m);  
Another term of comparison used for evaluating the quality of the generated DSMs were the requirements for the French Reference 3D(r): a 1 arc second DSM (\(\sim\)30m on the Equator, \(\sim\) 21 m at 45\({}^{\circ}\) of latitude) produced from SPOT-5/HRS satellite's stereoscopic data by IGN and Spot Image. Its specifications are an absolute horizontal CE90 of 15 m and an elevation absolute LE90 of 10 m for slopes lower than 20%, 18 m for slopes included in 20% and 40% and 30 m for slopes greater than 40% [17]. Finally, the 90 m resolution DSMs were also compared to the low-resolution SRTM90 DSM available for Eurasia. The comparison of the Catrosat-1 models and reference data was carried on as a 2.5D comparison, where the difference in heights was computed under the hypothesis of same geolocation for the Cartosat-1 generated and reference DSMs. The accuracy of Cartosat-1 DSMs was tested in terms of both first and second order statistics of residuals (mean and standard deviation), RMSE and LE90, all of them computed from data and not derived under hypothesis of Gaussian distribution of data.