# Evaluation of a Framework for Robust Image Reversible Watermarking
## 3 Results and Discussions
### Framework  
As described in Section 2, the framework consists of two main stages, a fragile reversible watermarking stage and a self-recovery stage. This section evaluates the framework through each possible combination of fragile reversible watermarking and self-recovery schemes. Table 2 shows the perceptual distortion performance for each scheme in detail. The framework was evaluated using six different configurations by combining the three selected fragile reversible watermarking and the two self-recovery schemes. Table 3 shows the results in terms of visual transparency for each configuration; the mean, standard deviation, minimum, and maximum values for PNSR and Watson metrics are presented. The robustness of the framework depends only on the self-recovery stage; therefore, no experimentation was carried out to observe the robustness of each configuration. As it is possible to observe from Table 2, fragile reversible watermarking schemes hold low perceptual distortion; thus, self-recovery schemes produce high perceptual distortion levels. This behavior is due to self-recovery schemes that need to embed considerable image information to have reconstruction capacities. Table 3 shows that the perceptual distortion \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Work**} & \multicolumn{4}{c}{**PSNR (dB)**} & \multicolumn{4}{c}{**Watson**} \\ \cline{3-10}  & & \(\mu\) & \(\sigma\) & **min** & **max** & \(\mu\) & \(\sigma\) & **min** & **max** \\ \hline F1 & [23] & 47.03 & \(\pm\)2.84 & 39.68 & 56.40 & 0.1433 & \(\pm\)0.0032 & 0.0007 & 0.0905 \\ F2 & [24] & 65.35 & \(\pm\)0.03 & 65.21 & 65.48 & 0.0016 & \(\pm\)0.0015 & 0.0006 & 0.0271 \\ F3 & [25] & 68.84 & \(\pm\)0.04 & 68.72 & 69.00 & 0.0003 & \(\pm\)0.0002 & 0.0002 & 0.0027 \\ \hline S1 & [26] & 29.57 & \(\pm\)4.10 & 20.17 & 46.98 & 0.1350 & \(\pm\)0.0675 & 0.0169 & 0.4146 \\ S2 & [27] & 37.90 & \(\pm\)0.12 & 36.78 & 38.71 & 0.0679 & \(\pm\)0.0316 & 0.0422 & 0.7103 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Perceptual distortion performance for fragile reversible watermarking (F1, F2, and F3) and self-recovery schemes (S1 and S2). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Configurations**} & \multicolumn{4}{c}{**PSNR (dB)**} & \multicolumn{4}{c}{**Watson**} & \multirow{2}{*}{**Payload (bits)**} \\ \cline{2-2} \cline{4-9}  & \(\mu\) & \(\sigma\) & **min** & **max** & \(\mu\) & \(\sigma\) & **min** & **max** \\ \hline F1-S1 & 29.02 & \(\pm\)4.51 & 20.25 & 40.34 & 0.1433 & \(\pm\)0.0830 & 0.0271 & 0.3953 & 5k \\ F1-S2 & 37.34 & \(\pm\)0.33 & 36.34 & 37.90 & 0.0688 & \(\pm\)0.0497 & 0.0497 & 0.4546 & 5k \\ F2-S1 & 29.56 & \(\pm\)4.09 & 20.17 & 46.76 & 0.1355 & \(\pm\)0.0675 & 0.0174 & 0.4145 & 10k \\
**F2-S2** & **37.90** & \(\pm\)0.13 & 36.53 & 38.74 & **0.0678** & \(\pm\)0.0313 & 0.0419 & 0.7022 & 10k \\ F3-S1 & 32.39 & \(\pm\)3.87 & 23.10 & 46.13 & 0.0985 & \(\pm\)0.0459 & 0.0202 & 0.2977 & 10k \\ F3-S2 & 37.89 & \(\pm\)0.12 & 36.90 & 38.90 & 0.0678 & \(\pm\)0.0199 & 0.0420 & 0.3357 & 10k \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Perceptual distortion performance for framework configuration. The best configuration in terms of average PSNR and Watson values is highlighted in bold. Figure 7: Example of image perfect restoration after a 10% attack. (**a**) Watermarked image, (**b**) attacked image, and (**c**) restored image. due to the framework is very close to the distortion due to the self-recovery scheme used in the configuration; in this table, the best configuration in terms of average PSNR and Watson values is highlighted in bold, which is the combination of the fragile reversible scheme [24] and the self-recovery [27]. However, additional experimentation was carried out to corroborate the framework's performance in terms of perceptual distortion. A fragile reversible watermarking scheme with high perceptual distortion was incorporated into the framework, and the perceptual distortion of the framework was measured.