## 3 Results
### Testing Results--Data 3  
Compared to the previous two datasets, the character of Data 3 differs in the sense of having a lot of details with sharp edges, which calls for a higher quality of the resulting model (diluted point cloud). The original resolution of the point cloud is also higher than in the previous cloud (better than 0.005 m). The data includes highly detailed reliefs, such  
Figure 9: Details of the Data 2 point cloud: (**a**) original cloud, (**b**) differences between the cloud acquired by uniform dilution with a = 0.02 m and the original point cloud, (**c**) point cloud after uniform dilution with a = 0.01 m, (**d**) differences between the cloud acquired by uniform dilution with a = 0.01 m and the original point cloud, (**e**) point cloud after a = 0.01 m b = 0.10 m progressive dilution (approximately the same number of points in the cloud as for uniform dilution 0.02 m), (**f**) differences between the cloud acquired by progressive dilution with a = 0.01 m b = 0.10 m and the original point cloud.  
as the coat of arms in the middle and decorations of the columns, as well as practically flat surfaces on the feet of the columns or directly on the building walls. The areas covering the cylindrical parts of columns are slightly curved. Figure 10 shows the original point cloud colored according to the \(T\) variable. The \(E_{3}\) calculation on a standard laptop took 2.2 s, the transformation of \(E_{3}\) to \(T\) is practically immediate, and the dilution took 0.9 s.  
The results of dilution in Data 3 are similar to the other datasets (see Figure 11 and Table 4). Figure 12 shows a detail of the Data 3 cloud. The detail contains areas of various flatness/ruggedness/curvature (flat wall, cylindrical parts of the columns with various radiuses, and very dense areas representing fine details in the stucco reliefs).  
Figure 12e clearly shows the level to which the flat surfaces can be diluted without loss of detail when using progressive dilution on well-preserved objects with plaster. Again, the loss of detail in complicated areas is most pronounced when a is increased (Figure 12b). Comparing the uniform dilution and progressive dilution with the same a, we can see only a very slight decrease in detail accuracy while reducing the point cloud size by more than 50%.  
Figure 10: Data 3—original point cloud colored according to the \(T\) values; red—flatest parts, blue—most curved/rugged parts.  
Figure 11: Data 3—examples of dilution: a = 0.005 m in all cases; (**a**) uniform dilution; (**b**) b = 0.010 m\({}_{2}\) (c) b = 0.025 m; (**d**) b = 0.050 m.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**a [m]** & **b [m]** & \
\begin{tabular}{c} **Points in** \\ **the Cloud** \\ \end{tabular} & **\% Original 1** & **RMSD [m]** &
\begin{tabular}{c} **RMSD\({}_{\text{E}}\)** \\ **[m]** \\ \end{tabular} & **\% Uniform 2** \\ \hline original & - & 1,470,249 & 100 & - & - & - \\ \hline
0.005 & uniform & 651,345 & 44.3 & 0.0004 & 0.0005 & 100.0 \\
0.005 & 0.010 & 506,966 & 34.5 & 0.0004 & 0.0005 & 77.8 \\
0.005 & 0.015 & 436,672 & 29.7 & 0.0004 & 0.0005 & 67.0 \\
0.005 & 0.025 & 369,672 & 25.1 & 0.0005 & 0.0006 & 56.8 \\
0.005 & 0.050 & 291,500 & 19.8 & 0.0006 & 0.0007 & 44.8 \\ \hline
0.01 & uniform & 181,235 & 12.3 & 0.0009 & 0.0009 & 100.0 \\
0.01 & 0.02 & 156,035 & 10.6 & 0.0009 & 0.0010 & 86.1 \\
0.01 & 0.03 & 140,215 & 9.5 & 0.0010 & 0.0010 & 77.4 \\
0.01 & 0.05 & 119,166 & 8.1 & 0.0011 & 0.0011 & 65.8 \\ \hline
0.02 & uniform & 49,600 & 3.4 & 0.0021 & 0.0021 & 100.0 \\
0.02 & 0.04 & 42,539 & 2.9 & 0.0022 & 0.0022 & 85.8 \\
0.02 & 0.06 & 38,153 & 2.6 & 0.0024 & 0.0024 & 76.9 \\
0.02 & 0.10 & 31,709 & 2.2 & 0.0046 & 0.0047 & 63.9 \\ \hline \hline \end{tabular} \({}^{1}\) % original—the percentage of points relative to the original cloud. 2 % uniform—the percentage of points relative to the uniformly diluted cloud, with respective a value.  
\end{table}
Table 4: Results of dilution of the Data 3 cloud—numbers of points and RMSDs (R = 0.05 m).