## 4 Experimental Results and Discussion
### Imperceptibility Test  
Imperceptibility is an important characteristic for all DIW applications. For a good watermarking scheme, the photographic quality of the cover and watermarked images should be almost the same. To evaluate the imperceptibility of the proposed scheme, subjective (qualitative) and objective (quantitative) analysis is carried out. Test cover images and corresponding watermarked images are shown in Figures 10 and 11, respectively. Subjective analysis of the cover image and its corresponding watermarked images exhibit no significant change to HVS (Human Visual System). This observation can be affirmed from images in Figures 10 and 11. Furthermore, objective analysis for the imperceptibility performance is analyzed using Mean Square Error (MSE), Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Metric (SSIM). MSE is a statistic measure to estimate the imperceptibility of watermarking scheme from the square of Euclidian distance. It estimates the error between the original and watermarked image. The mathematical relation for MSE shown in Equation (9):  
\[MSE=\frac{1}{M\times N}\sum_{r=1}^{M}\sum_{c=1}^{N}[C(r,c)-C_{1}(c,r)]^{2} \tag{9}\]  
where \(C\) is Cover image, and \(C_{1}\) is a watermarked image. PSNR is a good measure of pixel difference between two images. It is calculated using relations in Equation (10):  
\[PSNR=10\;\;log\;\;10\bigg{(}\frac{255^{2}}{MSE}\bigg{)} \tag{10}\]  
SSIM is a measure of three image features as luminance (ll), brightness (bb), structure (ss), and it is in accordance with the HVS. The mathematical relation for SSIM is shown in Equation (11):  
\[SSIM=[ll(C,C_{1}).\;\;bb(C,C_{1}).\;\;ss(C,C_{1})] \tag{11}\]  
\[ll(C,C_{1})=\frac{2C_{mean}*C_{mean}}{C^{2}{}_{mean}+{C_{1}}^{2}{}_{mean}}\]  
\[bb(C,C_{1})=\frac{2C_{var}*C_{1 var}}{C^{2}{}_{var}+{C_{1}}^{2}{}_{var}}\]  
\[ss(C,C_{1})=\frac{CC_{1 var}}{C_{var}+C_{1 var}}\]  
Figure 10: Grayscale cover images (1–6), color cover images (7–12) and binary watermark (13). where \(C_{mean}\), \(C_{1 mean}\) as a mean of \(C,C_{1}\), respectively; \({C^{2}}_{var}\), \({C_{1}}^{2}_{var}\) as variance of \(C,C_{1}\) and \(CC_{1 cvar}\) as co-variance of \(CandC_{1}\). Experiments are performed on different cover images with adaptively generated ISF (a). PSNR, SSIM, MSE and ISF values for the images shown in Figure 10 are tabulated in Table 1. It can be observed from Table 1 that, for all grayscale images, PSNR is above 51 dB and the average is 52.16 dB. For color images, PSNR is above 56 dB and the average is 57.89 dB. For both grayscale and color images, PSNR is greater than the threshold value of 37 dB and the average error rate is minimal as the MSE value is low. SSIM for grayscale images are above 0.9600 and the average is 0.9754, whereas SSIM for color images is above 0.9991, and the average is 0.9988. For all test cover images, SSIM is approaching the ideal value of 1. The proposed scheme shows higher performance for \"Tulips\" image having PSNR = 60.85 dB with SSIM = 1. Further imperceptibility performance of the proposed scheme is evaluated for 50 images of different modalities taken from the USC-SIPI dataset [36], and the imperceptibility performance (PSNR, SSIM, MSE) is provided in Table 2. From the table, it can be observed that, for 50 images, PSNR varies between 51.42 dB (for the image Sail boat) to 58.47 dB (for the image Pixel ruler) and an average of 51.55 dB. MSE varies between 0.5907 (for the image Stream and Bridge) to 0.0899 (for the image Jelly bean) and an average of 0.3813. SSIM varies between 0.6337 (for the image Resolution chart) to 0.9999 (for the image Grass) and an average of 0.9767. It is observed that, for the image \"Pixel Ruler\", the proposed scheme shows higher PSNR (58.47 dB) and low MSE (0.0924). Subjective and objective analysis of imperceptibility shows that  
Figure 11: Watermarked images: Grayscale (**1–6**), Color (**7–12**) and extracted watermark images (**a–I**). the proposed scheme has high imperceptibility for various image modalities.