# Comparison of Different Algorithms to Orthorectify WorldView-2 Satellite Imagery
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**3D RPFs with RPCs**} & \multicolumn{1}{c}{**Min**} & \multicolumn{1}{c}{**Max**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**St. dev.**} & \multicolumn{1}{c}{**RMS**} \\ \hline \multirow{6}{*}{DEM 1 m} & GCPs: 45 & 0.103 & 5.499 & 1.513 & 1.076 & 1.857 \\  & CPs: 15 & 0.231 & 2.121 & 1.237 & 0.604 & 1.377 \\  & GCPs: 60 & 0.080 & 5.413 & 1.576 & 1.124 & 1.935 \\  & CPs: 15 & 0.407 & 1.769 & 1.109 & 0.444 & 1.195 \\  & GCPs: 75 & 0.047 & 5.509 & 1.481 & 1.097 & 1.843 \\  & CPs: 15 & 0.318 & 1.844 & 1.072 & 0.454 & 1.164 \\ \hline \multirow{6}{*}{DEM 20 m} & GCPs: 45 & 0.285 & 19.997 & 2.889 & 3.406 & 4.466 \\  & CPs: 15 & 0.522 & 3.233 & 1.863 & 1.030 & 2.129 \\ \cline{1-1}  & GCPs: 60 & 0.076 & 20.031 & 2.657 & 2.994 & 4.003 \\ \cline{1-1}  & CPs: 15 & 0.425 & 3.853 & 1.744 & 1.040 & 2.030 \\ \cline{1-1}  & GCPs: 75 & 0.099 & 20.846 & 2.286 & 2.655 & 3.504 \\ \cline{1-1}  & CPs: 15 & 0.157 & 4.292 & 1.644 & 1.105 & 1.981 \\ \hline \multirow{6}{*}{DEM 75 m} & GCPs: 45 & 0.011 & 22.695 & 3.374 & 3.668 & 4.984 \\ \cline{1-1}  & CPs: 15 & 0.636 & 5.965 & 3.238 & 1.561 & 3.595 \\ \cline{1-1}  & GCPs: 60 & 0.190 & 24.263 & 3.537 & 4.225 & 5.510 \\ \cline{1-1}  & CPs: 15 & 0.812 & 5.581 & 3.401 & 1.580 & 3.750 \\ \cline{1-1}  & GCPs: 75 & 0.041 & 23.955 & 3.414 & 3.905 & 5.187 \\ \cline{1-1}  & CPs: 15 & 1.004 & 5.678 & 3.254 & 1.569 & 3.613 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Residuals (in meters) obtained for GCPs (45-60-75) and CPs using RPFs with RPC file. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**3D RPFs with RPCs**} & \multicolumn{1}{c}{**Min**} & \multicolumn{1}{c}{**Max**} & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**St. dev.**} & \multicolumn{1}{c}{**RMS**} \\ \hline \multirow{6}{*}{DEM 1 m} & GCPs: 0 & - & - & - & - & - \\  & CPs: 15 & 1.420 & 4.612 & 3.096 & 1.057 & 3.272 \\  & GCPs: 5 & 0.344 & 1.496 & 0.902 & 0.492 & 1.027 \\  & CPs: 15 & 0.366 & 4.989 & 2.710 & 1.438 & 3.068 \\  & GCPs: 10 & 0.129 & 3.538 & 1.397 & 0.945 & 1.687 \\  & CPs: 15 & 0.077 & 4.592 & 2.059 & 1.347 & 2.461 \\  & GCPs: 15 & 0.536 & 4.132 & 1.685 & 1.026 & 1.973 \\  & CPs: 15 & 0.234 & 3.036 & 1.450 & 0.864 & 1.688 \\ \hline \multirow{6}{*}{DEM 20 m} & GCPs: 0 & - & - & - & - & - \\  & CPs: 15 & 2.016 & 5.930 & 3.798 & 1.191 & 3.980 \\  & GCPs: 5 & 0.728 & 3.882 & 2.475 & 1.109 & 2.712 \\  & CPs: 15 & 0.573 & 7.175 & 2.190 & 1.653 & 2.744 \\  & GCPs: 10 & 1.259 & 10.378 & 3.492 & 2.640 & 4.378 \\  & CPs: 15 & 0.245 & 4.172 & 2.021 & 1.063 & 2.283 \\  & GCPs: 15 & 0.334 & 10.395 & 2.594 & 2.558 & 3.643 \\  & CPs: 15 & 0.380 & 4.036 & 2.027 & 1.082 & 2.298 \\ \hline \multirow{6}{*}{DEM 75 m} & GCPs: 0 & - & - & - & - & - \\  & CPs: 15 & 1.139 & 7.366 & 4.255 & 1.844 & 4.638 \\ \cline{1-1}  & GCPs: 5 & 0.795 & 5.510 & 2.832 & 1.818 & 3.366 \\ \cline{1-1} \cline{2-6}  & CPs: 15 & 0.336 & 9.639 & 2.960 & 2.750 & 4.041 \\ \cline{1-1}  & GCPs: 10 & 0.537 & 8.658 & 3.537 & 2.577 & 4.376 \\ \cline{1-1}  & CPs: 15 & 0.577 & 7.217 & 3.202 & 1.897 & 3.722 \\ \cline{1-1}  & GCPs: 15 & 0.427 & 8.342 & 2.946 & 2.316 & 3.747 \\ \cline{1-1}  & CPs: 15 & 0.623 & 6.817 & 3.171 & 1.975 & 3.735 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Residuals (in meters) obtained for GCPs (0-5-10-15) and CPs using rational polynomial functions (RPFs) with rational polynomial coefficient (RPC) file. Tables 6 and 7 show how [PERSON]'s rigorous model obtains a good performance using a low number of GCPs and a high-resolution DEM (e.g., with 15 GCPs, RMS residuals for CPs was 4.129 m using DEM with a 75 m cell size and 1.737 m using DEM with a 1 m cell size). Table 8 reports the results obtained using the combination of RPF and PF algorithms. The GCPs used in this case are illustrated in Figure 6. This approach achieves low residuals, comparable with the WV-2 cell size as well as avoiding other geometrical distortions associated with higher-order PFs (i.e., twist with second-order).