## 3 Results
### Dense Image Matching (DIM)
#### 3.2.1 Analysis Based on Reference Points  
A digital elevation model (DEM) with a pixel size of 10 cm was generated in ESRI ArcGIS Pro (ver. 2.8), rasterizing each image-based DIM point cloud using the binning maximum interpolation type and void fill method using the nearest neighbor. The elevation data were compared with available 110 GNSS measurements (the points not used in the AT process). Results are reported in Table 5 and visualized on the histogram in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Metashape**} & \multicolumn{2}{c}{**Inpho**} \\ \hline  & **Dataset** & **Consumer** & **Photogram.** & **Consumer** & **Photogram.** \\ \hline \multirow{4}{*}{**Ground Point**} & X [m] & 0.140 & 0.126 & 0.250 & 0.112 \\  & Y [m] & 0.128 & 0.126 & 0.302 & 0.138 \\  & Z [m] & 0.127 & 0.124 & 0.157 & 0.097 \\  & XY [m] & 0.189 & 0.178 & 0.392 & 0.178 \\  & Total [m] & 0.228 & 0.217 & 0.422 & 0.202 \\  & Image [pix] & 0.865 & 0.741 & 0.914 & 0.602 \\ \hline \multirow{4}{*}{**Check Point**} & X [m] & 0.198 & 0.134 & 0.433 & 0.126 \\  & Y [m] & 0.112 & 0.116 & 0.229 & 0.098 \\ \cline{1-1}  & Z [m] & 0.276 & 0.166 & 0.231 & 0.116 \\ \cline{1-1}  & XY [m] & 0.227 & 0.177 & 0.490 & 0.160 \\ \cline{1-1}  & Total [m] & 0.358 & 0.242 & 0.542 & 0.197 \\ \cline{1-1}  & Image [pix] & 0.899 & 0.573 & 0.914 & 0.602 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The AT accuracy for the consumer-grade and photogrammetric datasets.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & \multicolumn{2}{c}{**Photogrammetric**} & \multicolumn{2}{c}{**Consumer-Grade**} \\ \hline
**Parameter** & **Value** & **Error** & **Value** & **Error** \\ \hline
**F** & 213.75 mm & - & 213.75 mm & - \\
**Cx** & \(-\)0.37228 px & 0.016 & \(-\)0.47829 px & 0.044 \\
**Cy** & \(-\)0.40745 px & 0.017 & \(-\)0.97128 px & 0.049 \\
**B1** & 0.01994 & 0.00082 & \(-\)0.51154 & 0.00190 \\
**B2** & \(-\)0.02347 & 0.00078 & \(-\)0.68536 & 0.00180 \\
**K1** & \(-\)0.00422 & 0.00006 & \(-\)0.00725 & 0.00013 \\
**K2** & 0.01656 & 0.00028 & 0.03045 & 0.00062 \\
**K3** & \(-\)0.01965 & 0.00040 & \(-\)0.03965 & 0.00088 \\
**P1** & 0.00006 & 0.00003 & 0.00072 & 0.00001 \\
**P2** & \(-\)0.00005 & 0.00002 & \(-\)0.00004 & 0.00001 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results (values and estimated errors) of the self-calibration executed in Metashape on the photogrammetric and consumer-grade/regular datasets.  
The results do not show significant differences. The mean of height differences varies between 0 and 3 cm, which proves that there is no systematic error (constant offset between surfaces). Only the photogrammetric dataset processed with Inpho at 3 pix obtained a higher average value of almost 6 cm.  
The RMSE values for the photogrammetric set in both software are in the range of 20-22.5 cm. The RMSE for the regular dataset in Inpho reaches values closer to those of the photogrammetric dataset, 20.7-23.7 cm, while in Metashape, it is higher--29.1-30.7 cm. This may also be caused by the fact that these point clouds are sparser than the Inpho results. The maximum and minimum values do not necessarily indicate the poor quality of the performed dense image matching; it could also be due to terrain changes between the historical images (1986) and the reference data (2012).