# Evaluation of a Framework for Robust Image Reversible Watermarking
## 4 Conclusions  
In this study, the framework proposed in [20] was evaluated using ten different configurations to determine its perceptual distortion and robustness performance behavior.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Expansion \(n\)**} & \multicolumn{4}{c}{**PSNR (dB)**} & \multicolumn{4}{c}{**[PERSON]**} \\ \cline{3-10}  & & \(\mu\) & \(\sigma\) & **min** & **max** & \(\mu\) & \(\sigma\) & **min** & **max** \\ \hline C1 & 2 & 26.51 & \(\pm\)6.76 & 7.93 & 49.92 & 0.1673 & \(\pm\)0.1657 & 0.0118 & 2.8645 \\ C2 & 12 & 15.24 & \(\pm\)3.37 & 6.25 & 27.83 & 0.7331 & \(\pm\)0.3117 & 0.1402 & 4.3541 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Perceptual distortion performance of [35].  
\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**} \\ \cline{2-10}  & & \(\mu\) & \(\sigma\) & **min** & **max** & \(\mu\) & \(\sigma\) & **min** & **max** \\ \hline C1-S1 & 21.74 & \(\pm\)5.11 & 7.89 & 40.70 & 0.3164 & \(\pm\)0.2309 & 0.0351 & 3.3922 \\ C1-S2 & 25.78 & \(\pm\)5.88 & 7.92 & 37.65 & 0.1983 & \(\pm\)0.1686 & 0.0539 & 2.9249 \\ C2-S1 & 12.40 & \(\pm\)2.59 & 6.15 & 22.66 & 1.0504 & \(\pm\)0.3784 & 0.2753 & 4.9221 \\ C2-S2 & 15.21 & \(\pm\)3.34 & 6.55 & 27.44 & 0.7391 & \(\pm\)0.3116 & 0.1518 & 4.3353 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Perceptual distortion performance for framework configuration using [35] as the fragile reversible watermarking scheme.  
Using the appropriate reversible and self-recovery schemes within the framework makes it possible to achieve high robustness to content replacement attacks. At the same time, perceptual distortion is kept at practical levels. Moreover, an expression that approximated the framework performance in terms of perceptual distortion was proposed. The findings of this study will help the fast evaluation of reversible watermarking and self-recovery schemes to provide reversible watermarking robust to content replacement attack as the approximate perceptual distortion can be estimated by (20) and robustness is only due to the self-recovery stage.  
Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON]; software, [PERSON] and [PERSON]; validation, [PERSON], [PERSON] and [PERSON]; formal analysis, [PERSON] and [PERSON]; investigation, [PERSON] and [PERSON]; resources, [PERSON]-U.; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON] and [PERSON]; funding acquisition, [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported by the project 2017-01-7092 from CONACyT, Mexico.  
Not applicable.  
In this study, 2000 gray-level images from the BOWS 2 [34] data set were used. The BOWS 2 data set is freely available in [[http://bows2.ec-lille.fr](http://bows2.ec-lille.fr)]([http://bows2.ec-lille.fr](http://bows2.ec-lille.fr)) (last access: 13 June 2022).  
The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.