# Security Protection of 3D Models of Oblique Photography by Digital Watermarking and Data Encryption
## 5 Experimental Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Vertex Coordinates**} & \multicolumn{3}{c}{**Texture Coordinates**} \\ \cline{2-7}  & **SNR** & **PSNR** & **Haousdorff** & **SNR** & **PSNR** & **Haousdorff** \\ \hline M-1 & 182.800 & 184.579 & \(1\times 10^{-6}\) & 121.259 & 126.085 & \(1\times 10^{-6}\) \\ \hline M-2 & 183.972 & 185.334 & \(1\times 10^{-6}\) & 121.070 & 125.944 & \(1\times 10^{-6}\) \\ \hline M-3 & 183.731 & 185.263 & \(1\times 10^{-6}\) & 120.449 & 125.234 & \(1\times 10^{-6}\) \\ \hline M-4 & 165.106 & 149.681 & \(1\times 10^{-6}\) & 121.806 & 126.648 & \(1\times 10^{-6}\) \\ \hline M-5 & 170.467 & 174.429 & \(1\times 10^{-6}\) & 121.420 & 126.067 & \(1\times 10^{-6}\) \\ \hline M-6 & 171.666 & 174.594 & \(1\times 10^{-6}\) & 121.848 & 126.489 & \(1\times 10^{-6}\) \\ \hline M-7 & 169.355 & 152.655 & \(1\times 10^{-6}\) & 121.755 & 126.459 & \(1\times 10^{-6}\) \\ \hline M-8 & 185.329 & 186.308 & \(1\times 10^{-6}\) & 122.954 & 127.740 & \(1\times 10^{-6}\) \\ \hline M-9 & 182.411 & 181.094 & \(1\times 10^{-6}\) & 122.424 & 127.230 & \(1\times 10^{-6}\) \\ \hline M-10 & 164.001 & 166.509 & \(1\times 10^{-6}\) & 121.856 & 126.672 & \(1\times 10^{-6}\) \\ \hline Average & 175.884 & 174.045 & \(1\times 10^{-6}\) & 121.684 & 126.456 & \(1\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Imperceptibility evaluation. experiments, the mean PSNR and SNR values for vertex coordinate watermarking before and after embedding were 174.045 and 175.884, respectively. For texture coordinate watermarking, the mean PSNR and SNR values before and after embedding were 121.684 and 126.456, respectively. These values meet the imperceptibility requirements. Additionally, a smaller Hausdorff distance implies greater dissimilarity between two sets. As indicated in Table 4, this algorithm exhibits good imperceptibility. ### Analysis of Imperceptibility  
To verify the robustness of the algorithm, ten datasets were subjected to common data attacks, and the algorithm proposed in this paper was applied to extract watermarks from the attacked data. The normalized correlation (NC) value was used as a quantitative evaluation of the extraction results [33]. NC was commonly used to measure the similarity between two two-dimensional images. In this paper, the original watermark-containing model and the extracted watermark information after attack were compared to reflect the robustness of the research experimental results. Generally, a correlation coefficient greater than 70% can be considered as indicating that the algorithm had a certain degree of resistance to the attack [28]. The NC calculation is shown in Equation (22). \[NC=\frac{\sum_{i=1}^{L}w(i)w^{\prime}(i)}{\sqrt{\sum_{i=1}^{L}w^{2}(i)}\sqrt{ \sum_{i=1}^{L}w^{\prime 2}(i)}} \tag{22}\]  
In Equation (22), \(w(i)\) is the original watermark data; \(w^{\prime}(i)\) is the extracted watermark data after the watermark attack; \(L\) is the length of the watermark sequence. The threshold value selected in this article was 0.8. When the \(NC\) value is greater than this value, it is considered that the watermark robustness is strong. Compared with the two-dimensional model, the attack methods for the 3 DMOP were more complex and richer. In this study, common operations such as translation, cropping, rotation, noise attack, and simplification attack were used to perform attack experiments on the model.