# Evaluation of a Framework for Robust Image Reversible Watermarking
## 2 Evaluation of the Robust Framework for Robust Reversible Image Watermarking
### Selection of Schemes
#### 2.2.1 Fragile Reversible Watermarking Schemes
The embedding process first divides the intensity levels of the image into non-overlapped segments of equal size. Then, it generates a histogram for each block and identifies the intensity value of the peak pixel in each segment. The pixels from the original image are read, and then, \(k\) bits from the secret message \(M\) are embedded using a pixel substitution strategy on the peak pixels. Afterward, a location map is created, where a 1 is inserted if the pixel is a peak pixel or 0 otherwise. For the extraction process, the intensity values of the image are divided into non-overlapped segments of equal size in the same way as in the embedding process. The watermark image and the location map are read. The peak pixels of each reference segment are obtained; then the watermark bits are extracted, and the current pixel is replaced with the reference peak pixel. The scheme proposed in [25] expands the image size using an interpolation method that uses trigonometric functions; watermark bits are inserted in the interpolated pixels; this algorithm uses a location map. The extraction process recovers the watermark and eliminates the pixels generated by interpolation during embedding; therefore, the original image can be recovered. The embedding process first divides the host image into blocks of \(2\times 2\) pixels. Each block is transformed into blocks of \(3\times 3\) pixels through interpolation, using the following equations:  
\[B_{i}(1,1) =B_{o}(1,1)\] \[B_{i}(3,3) =B_{o}(2,2)\] \[B_{i}(2,2) =\sqrt{\frac{(B_{i}(1,2)^{2})+(B_{i}(3,2))^{2}}{2}}\] \[B_{i}(1,3) =B_{o}(1,2)\] \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]0 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]1 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]2 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]3 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]4  
where \(B_{o}\) is the original image block and \(B_{i}\) is the interpolated block. The new values are modified using the following trigonometric functions:\[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]5 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]6 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]7 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]8 \[K_{ph}=\Big{[}\Big{(}\frac{\alpha_{\text{maxP}}-\alpha_{\text{zero}}+1}{ \text{Partition level}}\Big{)}\Big{]}, \tag{2}\]9  
where \(B_{f}\) is the block modified by the trigonometric functions. Obtain 5 bits from the watermark \(M\), and insert them in the interpolated pixels. The extraction process divides the image into blocks of size \(3\times 3\) pixels, called \(C_{i}\). Then, calculate a new block using trigonometric functions, called \(C_{i}^{\prime}\). The watermark bits are extracted by subtracting the two blocks \(C_{i}-C_{i}^{\prime}\), and finally, the original image is obtained by eliminating the interpolated pixels.