# A Robust Multi-Watermarking Algorithm for Medical Images Based on DTCWT-DCT and Henon Map
## 4 Experiment and Analysis
### Geometrical Attacks
#### 4.2.3 Translation Attacks  
The watermarked image is moved down and left. When moved down by 22%, where the lower half of the image is lost, the extracted watermarks are still legible, and average NC values are still as high as 0.60. The average left-moving NC was 0.84. When moving left by 11%, the NC value was 0.69. Figure 20, Table 8, Figure 21 and Table 9 respectively show some test images and data moving down and left.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Rotation (Clockwise)** & \(\mathbf{5^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{15^{\circ}}\) & \(\mathbf{20^{\circ}}\) & \(\mathbf{25^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{45^{\circ}}\) \\ \hline PSNR (dB) & 16.19 & 13.49 & 12.70 & 12.38 & 12.16 & 11.90 & 11.25 & 10.95 \\ NC1 & 0.91 & 0.87 & 0.87 & 0.87 & 0.77 & 0.70 & 0.74 & 0.58 \\ NC2 & 0.93 & 0.90 & 0.90 & 0.90 & 0.86 & 0.83 & 0.86 & 0.74 \\ NC3 & 0.91 & 0.87 & 0.87 & 0.87 & 0.82 & 0.76 & 0.81 & 0.61 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Data of rotation attacks.  
Figure 19: Under scaling attacks: (**a**) Scaling factor 0.2; (**b**) the extracted watermark 1 under scaling factor 0.2; (**c**) the extracted watermark 2 under scaling factor 0.2; (**d**) the extracted watermark 3 under scaling factor 0.2; (**e**) Scaling factor 8.0; (**f**) the extracted watermark 1 under scaling factor 8.0; (**g**) the extracted watermark 2 under scaling factor 8.0; (**h**) the extracted watermark 3 under scaling factor 8.0.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Scaling Factor** & **0.2** & **0.4** & **0.5** & **0.8** & **1.2** & **2.0** & **4.0** & **8.0** \\ \hline NC1 & 0.57 & 0.86 & 1.00 & 0.86 & 0.96 & 1.00 & 1.00 & 1.00 \\ NC2 & 0.75 & 0.93 & 1.00 & 0.93 & 0.97 & 1.00 & 1.00 & 1.00 \\ NC3 & 0.61 & 0.90 & 1.00 & 0.90 & 0.96 & 1.00 & 1.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Data of scaling attacks.  
Figure 21: Under left translation attacks: (**a**) Left distance 7%; (**b**) the extracted watermark 1 under left distance 7%; (**c**) the extracted watermark 2 under left distance 7%; (**d**) the extracted watermark 3 under a left distance of 7%; (**e**) Left distance 11%; (**f**) the extracted watermark 1 under a left distance of 11%; (**g**) the extracted watermark 2 under a left distance of 11%; (**h**) the extracted watermark 3 under a left distance of 11%.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Down Distance (\%)** & **2** & **4** & **8** & **12** & **13** & **15** & **18** & **22** \\ \hline PSNR1(dB) & 15.33 & 12.59 & 11.96 & 11.31 & 11.20 & 10.83 & 10.32 & 9.99 \\ NC1 & 1.00 & 0.85 & 0.85 & 0.78 & 0.74 & 0.68 & 0.59 & 0.56 \\ NC2 & 1.00 & 0.91 & 0.91 & 0.88 & 0.84 & 0.79 & 0.73 & 0.70 \\ NC3 & 1.00 & 0.86 & 0.86 & 0.79 & 0.76 & 0.68 & 0.59 & 0.55 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Data of down translation attacks.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Left Distance (\%)** & **3** & **5** & **7** & **8** & **9** & **10** & **11** \\ \hline PSNR2(dB) & 12.28 & 11.38 & 11.14 & 10.80 & 10.56 & 10.31 & 9.80 \\ NC1 & 0.90 & 0.90 & 0.90 & 0.58 & 0.58 & 0.58 & 0.58 \\ NC2 & 0.97 & 0.97 & 0.97 & 0.81 & 0.81 & 0.81 & 0.81 \\ NC3 & 0.93 & 0.93 & 0.93 & 0.69 & 0.69 & 0.69 & 0.69 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Data of left translation attacks.  
Figure 20: Under down translation attacks: (**a**) Down distance 12%; (**b**) the extracted watermark 1 under down distance 12%; (**c**) the extracted watermark 2 under down distance 12%; (**d**) the extracted watermark 3 under a down distance of 12%; (**e**) Down distance 22%; (**f**) the extracted watermark 1 under a down distance of 22%; (**g**) the extracted watermark 2 under a down distance of 22%; (**h**) the extracted watermark 3 under a down distance of 22%.