# Evaluation of a Framework for Robust Image Reversible Watermarking
## 3 Results and Discussions
### Self-Recovery Schemes  
Each self-recovery scheme was tested using the images from the data set to evaluate the perceptual distortion and robustness of each scheme; the perceptual distortion is measured using the PSNR and Watson metrics. To determine the robustness of the schemes, content  
Figure 4: Fragile reversible watermarking schemes performance versus payload under PSNR metric.  
Figure 5: Fragile reversible watermarking schemes performance versus payload under the Watson metric.  
replacement attacks were applied to the watermarked images using different percentages to corroborate their robustness to a maximum percentage of attack, which is the same maximum as the ones reported by the authors. A content replacement attack takes a region of the image to attack and replaces it with another image with the same dimensions as the region being replaced. Although other common attacks exist, we focus on content replacement in this work since it is the attack that the two self-recovery schemes resist. Figure 6 shows an example of content replacement attacks using different percentages of substitution. Table 1 shows the mean value for the PSNR, and Watson's values were obtained from measuring the perceptual quality of the images watermarked with the self-recovery schemes; the maximum percentage of attack supported by each scheme is included in the last column. The maximum percentage of attack refers to the highest level of substitution where each scheme is capable of producing an image with perfect restoration, i.e., the scheme produces, as a result, an image containing the exact pixel values as the host image. Furthermore, the time complexity for processing one image is shown in Table 1.  
From Table 1, it is possible to observe that self-recovery strategies generate high distortion levels on the watermarked images; this is caused because a big amount of information from the image itself is embedded into the carrier image to guarantee self-recovery capacities. In terms of robustness, it can be observed that the scheme by [PERSON] and [PERSON] [26] achieves robustness for a maximum attack of 3.2%, while the scheme by [PERSON] et al. [27] achieves robustness for a maximum attack of 20%. It is worth mentioning that the scheme [27] can achieve robustness to higher percentages of attack at higher computational time cost; in this work, an optimized implementation of the scheme is used, which needs about 50 min to reconstruct an image tampered at 20%. Then, because of our limited computational resources, it was prohibitive to test [27] for percentages of tampering higher than 20%.  
The workflow for the restoration of the self-recovery scheme is as follows: during encoding, the self-recovery stage receives an image watermarked with the fragile reversible scheme and produces a second watermarked image that contains information for self-recovery, then that second watermarked image is attacked with a percentage of content replacement. In the decoding phase, the self-recovery stage receives the attacked image and extracts self-recovery information that allows perfect restoration, given that the attacked region is smaller than the maximum percentage supported; after perfect restoration, the image is passed to the fragile reversible stage to extract the secret message and recover the host image. Figure 7 depicts an example of perfect restoration after a 10% attack.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **PSNR dB** & **Watson** & **Max Attack** & **Time Complexity** \\ \hline [PERSON] and [PERSON] [26] & 29.57 & 0.135 & 3.2\% & 10 msec \\ [PERSON] et al. [27] & 37.90 & 0.067 & 20.0\% & 49.7 min \\ \hline \hline \end{tabular}
\end{table}
Table 1: Self-recovery schemes’ performance in perceptual, robustness, and time complexity terms.  
Figure 6: Content replacement attack: (**a**) 3.2%, (**b**) 10%, (**c**) 15%, and (**d**) 20%.