# Image Watermarking between Conventional and Learning-Based Techniques: A Literature Review
## 3 Performance Requirements in Digital Watermarking
### Imperceptibility  
The concept of imperceptibility is related to the visual system or auditory perception of watermark insertion in the host document. Therefore, in the case of images, the watermark should be invisible to a human observer in such a way that the inserted watermark does not affect the quality of the document [53]. The evaluation of the imperceptibility after watermark embedding is an important criterion for watermarking algorithms validation. For images, such an evaluation requires human visual system (HVS) analysis. Several objective measures have been proposed in the literature to measure the visual quality of a watermarked document.  
**Peak signal-to-noise ratio (PSNR):** PSNR is the most commonly used indicator for providing quantitative scores across the watermarked images. PSNR evaluates the invisibility requirements by comparing the similarity of the original image file to the watermarked one. The PSNR is defined as:  
\[PSNR=\log_{10}\left(\frac{d^{2}}{MSE}\right) \tag{4}\]  
where \(d\) is the maximum pixel value of the image and the maximum possible value for a pixel. For example, this is \(d=255\) if the image pixels are coded with 8 bits. \(MSE\) represents the mean square error, which is defined for two images using the following equation:  
\[MSE=\frac{1}{M\times N}\sum_{x=0}^{M-1}\sum_{y=0}^{N-1}(I_{0}(x,y)-I_{w}(x,y)) ^{2} \tag{5}\]  
where \(I_{0}\) and \(I_{w}\) are the original and watermarked image of dimension \(M\times N\), respectively. The higher PSNR value can be obtained with a low \(MSE\) value, indicating low degradation. In general, if the PSNR is greater than 40 dB, the watermark is considered invisible, while a value below 30 dB indicates significant distortions [54].  
**Structural similarity index model (SSIM):** The SSIM evaluates the structural similarity existing between two images. Unlike PSNR, which is based on the pixel-to-pixel difference between two images. The SSIM measure consists of combining three parameters: brightness, contrast, and structure comparison. It is computed on several windows of an image. The measure between two windows \(x\) and \(y\) is given by the following:  
\[SSIM(x,y)=[l(x,y)]^{\alpha}.[c(x,y)]^{\beta}.[s(x,y)]^{\gamma} \tag{6}\]  
where \(l(x,y)\), \(c(x,y)\), and \(s(x,y)\) represent the luminance function, contrast function, and structure comparison function, respectively. \(x\) and \(y\) are the pairs of local square windows of the original and the watermarked image, respectively, and the importance of each measurement is defined by the parameters \(\alpha\), \(\beta\), and \(\gamma\). Finally, the similarity between the reference image and the watermarked image is measured by the average of the SSIM calculated for each window and denoted by MSSIM:  
\[MSSIM(I_{0},I_{w})=\frac{1}{m}\sum_{i=0}^{m}SSIM(x_{i},y_{i}) \tag{7}\]  
where \(I_{0}\) and \(I_{w}\) are the original and the watermarked, respectively, and \(m\) represents the total number of windows. The range of MSSIM is from 0 to 1; therefore, the MSSIM value must be close to 1 to show high similarity between the two images.