# Imperceptible-Visible Watermarking to Information Security Tasks in Color Imaging
## 4 Experimental Results
### Performance Metrics for Image Quality Degradation, Imperceptibility, and Robustness  
To evaluate the performance of the proposed algorithm in terms of the watermarked image quality degradation, imperceptibility of the watermark pattern, and robustness against the common geometric and image processing attacks listed in Tables 2 and 3, the peak signal to noise ratio (PSNR), structural similarity index (SSIM) [38], normalized color difference (NCD) [39], normalized correlation (NC), and bit error rate (BER) are used. Image quality degradation is generally measured by the performance metric PSNR, as shown in Equation (17). \[PSNR(I_{k},I_{w})=10\log_{10}\ \ \frac{\max(I_{k}(p_{i}))^{2}}{MSE}, \tag{17}\]  
\[MSE(I_{k},I_{w})=\frac{1}{w_{Iw}\times h_{Iw}}\sum_{i=1}^{w_{Iw}\times h_{Iw}}[ I_{k}(p_{i})-I_{w}(p_{i})]^{2}, \tag{18}\]  
where MSE given by Equation (18) is the mean square error between the original \(I_{k}\) and the watermarked image \(I_{w}\), and \(w_{Iw}=w_{I}\) and \(h_{Iw}=h_{I}\) are the width and height of the watermarked image. Typically, when \(PSNR\)\(\in\) (37 dB, intf), it means that the embedding process generates a low-quality degradation in the watermarked image, and a value nearest to 0 dB represents a higher-quality degradation [41]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Attack** & **Specification** \\ \hline Rotation & Angle 45\({}^{\circ}\), [90\({}^{\circ}\),180\({}^{\circ}\),270\({}^{\circ}\)] \\ Rescaling & 0.75\(\times\), [0.9\(\times\), 1.1\(\times\), 1.5\(\times\)] \\ Translation with cropping & \(x=50\), \(y=50\); [\(x=-50\), \(y=-50\)] \\ Flip transformation & Horizontal—[Vertical] direction \\ Affine Transformation & [1.0,3.0,0.3,2.0,0,0,1] \\ Aspect ratio & [0.8,0,0.9,1.5,0.0,0.1] \\ Shearing & \(x\)-direction [1 0 0; 0.2 1 0; 0 0 1] \\ Radial & \\ \hline \hline \end{tabular} \(\dagger\) additional experimental results refer to [40].  
\end{table} 
Table 2: Common geometric attacks used in the experiment. Figure 9: Binary watermark patterns: (**a**) Owner logotype FI, (**b**) QR code level L, and (**c**) Owner logotype UNAM. The imperceptibility can be defined as a measure of similarity between the original and its corresponding watermarked image. In addition to the PSNR, other metrics to measure the imperceptibility are the SSIM and the NCD, where the SSIM represents an individual comparison of three image parameters such as luminance, contrast, and structure, as shown in (19). \[SSIM(I_{k},I_{w})=\frac{\left(2\mu_{I_{k}}\mu_{I_{w}}+C_{1}\right)\left(2\sigma_ {I_{k}},\ \ I_{w}+C_{2}\right)}{\left(\mu_{I_{k}}^{2}+\mu_{I_{w}}^{2}+C_{1}\right) \left(\sigma_{I_{k}}^{2}\sigma_{I_{w}}^{2}+C_{2}\right)}, \tag{19}\]  
where \(\mu_{I}\) and \(\mu_{I_{w}}\) are the mean value of \(I_{k}\) and \(I_{w}\), respectively, \(\sigma_{I,Iw}\) and \(\sigma^{2}_{X}\) are the corresponding covariance and variance between \(I_{k}\) and \(I_{w}\), respectively, and \(C_{1}=(k_{1}L)^{2}\) and \(C_{2}=(k_{2}L)^{2}\) are two constants used to stabilize the denominator, where \(k_{1}=0.01\), \(k_{2}=0.03\) and \(L=255\) correspond to the dynamic range of 8 bits per pixel. The NCD is another performance metric of imperceptibility that measures in the CIELAB color space the similarity between the original image \(I_{k}\) and its corresponding watermarked image \(I_{w}\); it is formulated as shown in (20). \[NCD(I_{k},I_{w})=\frac{\sum\limits_{x=1}^{h_{I_{w}}}\sum\limits_{y=1}^{w_{I_{ w}}}\left(\sqrt{\left(\Delta L(x,y)\right)^{2}+\left(\Delta a(x,y)\right)^{2}+ \left(\Delta b(x,y)\right)^{2}}\right)}{\sum\limits_{x=1}^{h_{I}}\sum\limits_{ y=1}^{w_{I}}\left(\sqrt{\left(L(x,y)\right)^{2}+\left(a(x,y)\right)^{2}+ \left(b(x,y)\right)^{2}}\right)}, \tag{20}\]  
where \(\Delta L(x,y)\), \(\Delta a(x,y)\), and \(\Delta b(x,y)\) of the numerator are the difference between the luminance \(L\) and the spaces \(a\) and \(b\) of the original image I and the watermarked image \(I_{w}\) at the position (\(x\),\(y\)). In the denominator \(L\), \(a\) and \(b\) are the original image color spaces.