# Robust Template-Based Watermarking for DIBR 3D Images
## 4 Experimental Results
### Robustness against Geometric Distortion  
A robustness test against geometric distortion was also conducted with the center, left and right images. We did not consider the case where a geometric attack occurred before the DIBR attack. If a geometric attack takes place before a DIBR attack, the image becomes unnatural. For example, depth is measured horizontally, so if the DIBR is applied after the image is rotated, pixel warping will occur in an unintended direction.  
Tables 9-12 show the average BER for the geometrically-distorted center, left and right images, and Figure 14 illustrates the average BER for the geometrically-distorted right image.  
[PERSON]'s method does not show good results against geometric distortion, because this method embeds the watermark in the DCT domain, which is vulnerable to geometric distortion.  
[PERSON]'s method shows good performance against scaling, but is weak to rotation, translation and shearing. This method does not lose synchronization information in scaling. However, the rotation, translation and shearing attacks break the block synchronization. This is because the block size is specified as the ratio of the image, such as \((width/M)\times(height/N)\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Translation**} & \multicolumn{3}{c}{**Proposed**} & \multicolumn{3}{c}{**[PERSON]**} & \multicolumn{3}{c}{**[PERSON]**} \\ \cline{2-10}  & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** \\ \hline
10 & **0.08** & **0.06** & **0.09** & 0.54 & 0.51 & 0.51 & 0.24 & 0.22 & 0.22 \\
20 & **0.07** & **0.05** & **0.08** & 0.53 & 0.50 & 0.53 & 0.55 & 0.55 & 0.55 \\
30 & **0.11** & **0.07** & **0.12** & 0.49 & 0.47 & 0.50 & 0.53 & 0.53 & 0.53 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Average BER for translation attack.  
Figure 14: Average BER for geometric distortion. This experiment was conducted on the right image.  
(**a**) Image size scaling; (**b**) image rotation; (**c**) image translation; (**d**) image shearing.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Shearing**} & \multicolumn{3}{c}{**Proposed**} & \multicolumn{3}{c}{**Lin**} & \multicolumn{3}{c}{**Kim**} \\ \cline{2-10}  & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** & **Left** & **Center** & **Right** \\ \hline
0.1 & **0.03** & **0.02** & **0.02** & 0.54 & 0.51 & 0.52 & 0.24 & 0.22 & 0.22 \\
0.2 & **0.03** & **0.03** & **0.03** & 0.48 & 0.53 & 0.49 & 0.53 & 0.50 & 0.51 \\
0.3 & **0.05** & **0.05** & **0.05** & 0.50 & 0.51 & 0.47 & 0.52 & 0.53 & 0.56 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Average BER for shearing attack.  
The proposed method shows good performance on this test, because it utilizes a template robust to geometric attacks. Since the images were recovered from geometric distortion using this template, the message watermark has a low error.  
Experiments were also conducted on the combination of geometric distortion in the proposed method. This experiments were conducted by combining two of rotation, translation and scaling, and the results are shown in Table 13. Rotation with translation and scaling with translation show good results. However, when rotation and scaling occur at the same time, the watermark signal is greatly weakened, so the error is higher than with other geometric combination attacks.