# Security Protection of 3D Models of Oblique Photography by Digital Watermarking and Data Encryption
## 5 Experimental Results and Analysis
### Analysis of Imperceptibility  
To quantitatively analyze the errors introduced by the model data before and after embedding the watermark, three commonly used evaluation metrics can be employed. These metrics include the Hausdorff distance, signal-to-noise ratio (SNR), and peak signal-to-noise ratio (PSNR). These metrics facilitate a quantitative evaluation between the original model and the watermarked model. The Hausdorff distance method is a commonly used \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clustering** & \multicolumn{2}{c}{**Number of Clustering Clusters**} & \multicolumn{2}{c}{**Number of Identical Clustering Clusters**} \\
**Algorithm** & **in the Original Data** & **in the Cropped Data** & **Clustering Clusters** \\ \hline DBSCAN & 30 & 17 & 17 \\ K-means & 18 & 18 & 0 \\ Mean-shift & 13 & 6 & 1 \\ Hierarchical & 10 & 10 & 0 \\ Agglomerative & 10 & 10 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of clusters before and after data clipping by different algorithms. Figure 6: Results before and after clustering with different clustering algorithms, with different colors representing distinct clusters. (**a,f**) show the clustering results before and after pruning using the DBSCAN clustering algorithm, (**b,g**) represent the results before and after pruning with the K-means clustering algorithm, (**c,h**) display the results before and after pruning with the mean-shift clustering algorithm, (**d,i**) demonstrate the results before and after pruning using the hierarchical clustering algorithm, and (**e,j**) showcase the results before and after pruning with the agglomerative clustering algorithm. method for comparing the similarity between two data sets. The Hausdorff distance \(H(A,B)\) between the original data \(A\) and the watermarked data \(B\) was defined as shown in Equation (17). The Hausdorff distance \(H(A,B)\) in Equation (18) is the single Hausdorff distance from set \(A\) to set \(B\), which first calculated the distance between each point \(a_{i}\) in set \(A\) and the point \(b_{i}\) with the minimum distance from the point in set \(B\), and then sorted the calculated distance set. The maximum value in the sequence was taken as the value of \(H(A,B)\). Equation (19) represents the calculation of \(H(B,A)\), which is similar to Equation (18). The smaller the Hausdorff distance \(H(A,B)\), the smaller the error of the model, and the better the imperceptibility of the watermark. \[H(A,B)=max\ (h(A,\ B),\ h(B,A)) \tag{17}\]  
\[h(A,\ B)=\underset{a\in A}{max\ \underset{b\in B}{min}}\|a-b\| \tag{18}\]  
\[h(B,\ A)=\underset{b\in B}{max\ \underset{a\in A}{min}}\|b-a\| \tag{19}\]  
The original coordinates were considered as normal signals, and the data that changed after embedding the watermark were considered as noise. The signal-to-noise ratio (SNR) reflects the ratio between the strength of the normal signal and the noise, and the peak signal-to-noise ratio (PSNR) can reflect the ratio between the maximum signal strength and the noise strength. The larger the values of SNR and PSNR, the smaller the change in the data caused by embedding the watermark, which indicates that the imperceptibility of the watermark is better. The calculation methods of SNR and PSNR are shown in Equations (20) and (21). \[SNR=10 log_{10}\left(\sum_{i=0}^{N}\|Z_{i}\|^{2}/\sum_{i=0}^{N}\|Z_{i}^{\prime} -Z_{i}\|^{2}\right) \tag{20}\]  
\[PSNR=10 log_{10}\left(\sum_{i=0}^{N}\|Z_{i}\|^{2}/\frac{1}{N}\sum_{i=0}^{N}\|Z_ {i}^{\prime}-Z_{i}\|^{2}\right) \tag{21}\]  
Using the above three parameters to quantitatively analyze the data before and after embedding the watermark, the calculation results are shown in Table 4.  
The threshold for PSNR and SNR was typically set at 28, and when the value is greater than 28, it is considered that the watermark performed well in imperceptibility [28]. In ten