# Comparison of Different Algorithms to Orthorectify WorldView-2 Satellite Imagery
## 3 Results and Discussion  
The positional accuracy of the primary panchromatic image was tested using 15 CPs. Figure 4 reports the CP distribution in the WV-2 primary panchromatic image. Table 1 shows the statistical values (minimum, maximum, mean, standard deviation, RMS) of errors in these CPs. The low level of positional accuracy of the primary image (RMS = 84.589 m) is evident compared with the pixel dimensions. The performance of each rectification was evaluated by the residuals obtained for GCPs and CPs in XY direction. Figure 5 illustrates the distribution of all GCPs datasets (5-10-15-45-60-75) in WV-2 primary panchromatic image. A homogenous distribution was attempted for each group of GCPs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Primary Panchromatic Image** & **Min** & **Max** & **Mean** & **St. dev.** & **RMS** \\ \hline CPs: 15 & 9.843 & 129.180 & 75.324 & 38.491 & 84.589 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Residuals (in meters) obtained for CPs in the primary WV-2 panchromatic image. Figure 4: 15 CP distribution in WV-2 primary panchromatic image. The coordinates reported are referred to as UTM/WGS84 (33 N—zone T) and are expressed in meters. For all the tests performed, 15 CPs (the same as the previous test on the primary image) were introduced. Statistical values of these errors are reported in the following tables. Table 2 shows how for both fourth- and fifth-order PFs, 60 GCPs produce better results than 45 GCPs while the introduction of another 15 GCPs leads to small increases in accuracy. However, the results are not suitable (RMS for CPs = 10-25 m) in terms of the image geometric resolution (0.5 m). Tables 3 and 4 show how the original RPC file supplied by image provider limits CP residuals using a low number of GCPs (i.e., when a DEM with a cell size of 1 m is used, only 5 GCPs mean that the RMS on CPs can be limited to 3.272 m). Although height accuracy is less important than planimetric accuracy, the influence of DEM resolution on elevation extraction is also evident (e.g., with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**2D PFs**} & \multicolumn{1}{c}{**Min**} & \multicolumn{1}{c}{**Max**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**St. dev.**} & \multicolumn{1}{c}{**RMS**} \\ \hline \multirow{6}{*}{4 th order} & GCPs: 45 & 0.460 & 46.009 & 11.080 & 9.826 & 14.810 \\  & CPs: 15 & 0.538 & 74.462 & 15.799 & 18.063 & 23.997 \\  & GCPs: 60 & 0.318 & 62.633 & 12.176 & 10.280 & 15.935 \\  & CPs: 15 & 0.424 & 22.891 & 10.930 & 7.051 & 13.007 \\  & GCPs: 75 & 0.672 & 65.419 & 11.076 & 9.836 & 14.813 \\  & CPs: 15 & 0.831 & 26.640 & 10.669 & 8.023 & 13.349 \\ \hline \multirow{6}{*}{5 th order} & GCPs: 45 & 0.320 & 34.806 & 7.515 & 7.459 & 10.589 \\  & CPs: 15 & 1.717 & 43.673 & 16.866 & 13.993 & 21.915 \\ \cline{1-1}  & GCPs: 60 & 0.252 & 49.394 & 9.533 & 8.484 & 12.761 \\ \cline{1-1}  & CPs: 15 & 1.584 & 27.137 & 9.342 & 7.164 & 11.773 \\ \cline{1-1}  & GCPs: 75 & 0.358 & 52.241 & 8.622 & 8.264 & 11.943 \\ \cline{1-1}  & CPs: 15 & 1.010 & 20.907 & 8.250 & 5.691 & 10.022 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Residuals (in meters) obtained for ground control points (GCPs) and CPs using polynomial functions. Figure 5: All GCP datasets (5-10-15-45-60-75) distribution in WV-2 primary panchromatic image. The coordinates reported are referred to as UTM/WGS84 (33 N—zone T) and are expressed in meters. 15 GCPs, the RMS residuals for CPs was 3.747 m using DEM with a 75 m cell size and 1.688 m using DEM with a 1 m cell size. Table 5 shows that to achieve good results a great number of GCPs as well as a high-resolution DEM are required to calculate RPCs.