# Photogrammetry-Based 3D Textured Point Cloud Models Building and Rock Structure Estimation
## 4 The Accuracy Verification of the 3D Point Cloud Model
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**No.**} & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline Distance between the total station and the measuring & & & & & & & & \\ pod (m) & & 10 & 10 & 10 & 10 & 30 & 50 & 100 \\ \hline Orientation obtained by & Dip direction & 277 & 9 & 93 & 192 & 285 & 274 & 313 \\ compass (\({}^{\circ}\)) & Dip & 53 & 53 & 54 & 51 & 50 & 50 & 54 \\ \hline Orientation calculated from & Dip direction & 277.20 & 10.19 & 93.78 & 192.59 & 286.09 & 275.90 & 314.88 \\ coordinates (\({}^{\circ}\)) & Dip & 52.63 & 53.67 & 54.14 & 51.08 & 50.83 & 50.55 & 55.25 \\ \hline \multirow{7}{*}{Distances obtained by vernier} & AB & & & & & & & \\  & BC & & & & & & & \\  & CD & & & & & & & \\  & DE & & & & & & & \\  & EF & & & & & & & \\  & FA & & & & & & & \\  & AG & & & & & & & \\  & GD & & & & & & & \\  & CG & & & & & & & \\  & GF & & & & & & & \\ \hline \multirow{7}{*}{Distances calculated from} & AB & 174.39 & 174.58 & 174.03 & 174.59 & 173.92 & 174.11 & 172.47 \\  & BC & 178.32 & 177.82 & 179.29 & 178.43 & 178.30 & 178.02 & 176.86 \\ \cline{1-1}  & CD & 245.71 & 246.10 & 245.32 & 246.45 & 246.28 & 244.90 & 249.10 \\ \cline{1-1}  & DE & 175.01 & 174.88 & 174.83 & 174.90 & 174.89 & 175.24 & 175.44 \\ \cline{1-1}  & EF & 173.23 & 173.27 & 173.63 & 173.19 & 173.08 & 172.57 & 173.98 \\ \cline{1-1}  & coordinates (mm) & FA & 239.96 & 240.31 & 239.07 & 241.05 & 239.90 & 240.12 & 239.61 \\ \cline{1-1}  & AG & 212.09 & 212.62 & 210.08 & 212.70 & 211.36 & 211.44 & 213.91 \\ \cline{1-1}  & GD & 217.07 & 217.09 & 217.77 & 217.10 & 217.42 & 216.48 & 216.26 \\ \cline{1-1}  & CG & 214.79 & 213.35 & 216.82 & 215.17 & 215.27 & 214.66 & 215.01 \\ \cline{1-1}  & GF & 208.78 & 209.78 & 208.04 & 208.93 & 208.40 & 209.00 & 207.49 \\ \hline Absolute values of orientation & Dip direction & 0.20 & 1.19 & 0.78 & 0.59 & 1.09 & 1.90 & 1.88 \\ differences (\({}^{\circ}\)) & Dip & 0.37 & 0.67 & 0.14 & 0.08 & 0.83 & 0.55 & 1.25 \\ \hline \multirow{7}{*}{Absolute values of distance} & AB & 0.23 & 0.04 & 0.59 & 0.03 & 0.70 & 0.51 & 2.15 \\  & BC & 0.22 & 0.72 & 0.75 & 0.11 & 0.24 & 0.52 & 1.68 \\ \cline{1-1}  & CD & 0.51 & 0.12 & 0.90 & 0.23 & 0.06 & 1.32 & 2.88 \\ \cline{1-1}  & DE & 0.01 & 0.14 & 0.19 & 0.12 & 0.13 & 0.22 & 0.42 \\ \cline{1-1}  & EF & 0.41 & 0.37 & 0.01 & 0.45 & 0.56 & 1.07 & 0.34 \\ \cline{1-1}  & FA & 0.14 & 0.21 & 1.03 & 0.95 & 0.20 & 0.02 & 0.49 \\ \cline{1-1}  & AG & 0.43 & 0.96 & 1.58 & 1.04 & 0.30 & 0.22 & 2.25 \\ \cline{1-1}  & GD & 0.15 & 0.13 & 0.55 & 0.12 & 0.20 & 0.74 & 0.96 \\ \cline{1-1}  & CG & 0.65 & 2.09 & 1.38 & 0.27 & 0.17 & 0.78 & 0.43 \\ \cline{1-1}  & GF & 0.44 & 0.56 & 1.18 & 0.29 & 0.82 & 0.22 & 1.73 \\ \cline{1-1}  & Mean value (mm) & & 0.32 & 0.53 & 0.82 & 0.36 & 0.34 & 0.56 & 1.33 \\ \hline \end{tabular}
\end{table} 
Table 1: Results of the outdoor experiment for the accuracy verification of the total station. The coordinates of a total of 30 feature points (corresponding to the numbers 1 to 30) on the slope (see Figure 4) were measured in Meshlab (after conducting the coordinate transformation) and in the field simultaneously. Feature points 1 to 4 are control points that were used for calculating the transformation matrix, while feature points 5 to 30 were employed for the accuracy verification of the 3D point cloud model. The mean value of the distances of the feature points 5 to 30 between the 2 sets of coordinates is 3.96 mm. Tables 2 and 3 list the length and the angle accuracy verification results, respectively, for the 3D point cloud model. As can be seen from the 2 tables, the absolute values of the length, dip, and dip direction differences calculated based on the 2 sets of coordinates are 1.57 mm, 0.38 degrees, and 0.42 degrees, respectively; therefore, the accuracy of the textured 3D point cloud model is high enough for the engineering application. It should be noted that the accuracy listed above is taking the coordinates obtained by the total station as a reference.