# Convolutional Neural Network Architecture for Recovering Watermark Synchronization
## 5 Experimental Results
### Application of Proposed Template to DIBR Watermarking Method  
We tested the robustness of the DIBR watermarking method against RST when the proposed template is applied. The experiment was conducted in three ways: (1) DT-CWT with template recovery, (2) DT-CWT with ground-truth recovery, and (3) Only DT-CWT method. All experiments used the right-view image rendered by DIBR. In other words, we measured the BER of images with DIBR  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Noise Variance**} \\ \hline
**Trans.** & **Recover** & **25** & **50** & **100** & **200** \\ \hline \multirow{2}{*}{3\%} & With template & 0.119 & 0.229 & 0.273 & 0.338 \\  & With GT & 0.1 & 0.198 & 0.23 & 0.275 \\ \hline \multirow{2}{*}{9\%} & With template & 0.163 & 0.249 & 0.289 & 0.354 \\  & With GT & 0.15 & 0.227 & 0.253 & 0.301 \\ \hline \multirow{2}{*}{15\%} & With template & 0.203 & 0.291 & 0.329 & 0.387 \\  & With GT & 0.19 & 0.263 & 0.289 & 0.324 \\ \hline \multirow{2}{*}{21\%} & With template & 0.255 & 0.328 & 0.364 & 0.427 \\  & With GT & 0.234 & 0.294 & 0.319 & 0.353 \\ \hline \multirow{2}{*}{27\%} & With template & 0.304 & 0.369 & 0.4 & 0.445 \\  & With GT & 0.284 & 0.338 & 0.359 & 0.378 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average BER for translation attack with Gaussian noise.  
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline  & \multicolumn{5}{c}{**Noise Variance**} \\ \hline
**Rot.** & **Recover** & **25** & **50** & **100** & **200** \\ \hline \multirow{2}{*}{10\({}^{\text{a}}\)} & With template & 0.174 & 0.233 & 0.268 & 0.304 \\  & With GT & 0.17 & 0.22 & 0.265 & 0.281 \\ \hline \multirow{2}{*}{30\({}^{\text{a}}\)} & With template & 0.138 & 0.205 & 0.258 & 0.288 \\  & With GT & 0.132 & 0.189 & 0.223 & 0.244 \\ \hline \multirow{2}{*}{50\({}^{\text{a}}\)} & With template & 0.169 & 0.241 & 0.28 & 0.314 \\  & With GT & 0.145 & 0.2 & 0.232 & 0.25 \\ \hline \multirow{2}{*}{70\({}^{\text{a}}\)} & With template & 0.204 & 0.297 & 0.333 & 0.387 \\  & With GT & 0.189 & 0.248 & 0.296 & 0.32 \\ \hline \multirow{2}{*}{90\({}^{\text{a}}\)} & With template & 0.081 & 0.204 & 0.254 & 0.33 \\  & With GT & 0.054 & 0.159 & 0.194 & 0.243 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average BER for rotation attack with Gaussian noise. GT denotes ground-truth.  
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline  & \multicolumn{5}{c}{**Noise Variance**} \\ \hline
**Scaling** & **Recover** & **25** & **50** & **100** & 200 \\ \hline \multirow{2}{*}{0.7} & With template & 0.089 & 0.173 & 0.235 & 0.275 \\  & With GT & 0.089 & 0.168 & 0.226 & 0.264 \\ \hline \multirow{2}{*}{0.9} & With template & 0.07 & 0.16 & 0.201 & 0.249 \\  & With GT & 0.061 & 0.163 & 0.197 & 0.244 \\ \hline \multirow{2}{*}{1.2} & With template & 0.068 & 0.161 & 0.207 & 0.241 \\  & With GT & 0.068 & 0.161 & 0.207 & 0.241 \\ \hline \multirow{2}{*}{1.5} & With template & 0.065 & 0.152 & 0.204 & 0.243 \\  & With GT & 0.065 & 0.152 & 0.204 & 0.243 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average BER for scaling attack with Gaussian noise.  
distortion and RST distortion simultaneously. DIBR parameters used in this test were the recommended values in [39].  
As shown in Figure 10, the DT-CWT-based DIBR watermarking method has a low BER for weak geometric distortions, similar to curvelet watermarking methods. However, as the degree of geometric distortion increases, the BER increases sharply.  
On the other hand, if the image is recovered using a template with the DT-CWT method, the watermark can be decoded well after the geometric distortion. The DT-CWT method recovered with a template has a slightly higher BER than that recovered with ground-truth because the template is disturbed by DIBR. However, since the error increase rate is insignificant, the proposed template can be considered robust to the new type of distortion, DIBR. These results show that the proposed template can give robustness against geometric attacks to newly proposed watermarking techniques.