# Security Protection of 3D Models of Oblique Photography by Digital Watermarking and Data Encryption
## 5 Experimental Results and Analysis
### Analysis of Imperceptibility
#### 5.2.4 Randomly Adding and Deleting Points in the Model  
A fixed proportion of random addition and deletion points were attacked on the model, with a random addition proportion of 10-30% and a deletion proportion of 1-10%. The experimental results are shown in Table 8. After applying noise attacks to the model, there was a certain degree of accuracy loss. The embedding feature selected for embedding the vertex coordinates watermark is the distance between the feature point and the virtual centroid. The coordinates of the virtual centroid depend on the coordinates of the feature point, so the vertex coordinates watermark is not affected when a small number of point clouds are added. When the proportion of point attacks exceeds 30%, the vertex coordinate watermark \(NC\) value is less than 0.8, which is not robust to the attack, but still allows for the identification of copyright information. Deleting points has a small impact on the vertex coordinates watermark. The embedding feature selected for embedding the texture coordinates watermark is the global feature, and the mapping relationship between the texture coordinates and the watermark is a many-to-one mapping. Therefore, it is basically immune to the image attack of adding or deleting points.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**3 DMOP**} & \multicolumn{3}{c}{**Translation (\(\mu\), Unit meter)**} & \multicolumn{3}{c}{**Rotate (\(\theta\), Unit: \({}^{\circ}\))**} \\ \cline{2-7}  & **1.5** & **3** & **15** & **3.25** & **30** & **90** \\ \hline M-1 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-2 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-3 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-4 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-5 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-6 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-7 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-8 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-9 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline M-10 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline Average & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 & NC = 1.0 \\ \hline \end{tabular}
\end{table}
Table 5: Normalized correlation coefficients after translation and rotation attacks.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cropping Ratio** & **Cropping Locations** & **NC for Vertex Coordinate Extraction Results** & **NC for Texture Coordinate Extraction Results** & **Extraction Successful** \\ \hline
30\% & & 0.9569688990161647 & 1.0 & \(\surd\) \\
40\% & & 0.951453182187509 & 1.0 & \(\surd\) \\
50\% & & 0.9403246919632546 & 1.0 & \(\surd\) \\
60\% & & 0.8944271909999159 & 1.0 & \(\surd\) \\
70\% & & 0.899434844341313 & 1.0 & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Normalized correlation coefficient after the clipping attack.