# A Hybrid Domain Color Image Watermarking Scheme Based on Hyperchaotic Mapping
## 3 The Proposed Watermarking Scheme
### Robustness Analysis
\begin{table}
\begin{tabular}{l c c c c c c} \hline
**Type of Attack** & **Airplane** & **Baboon** & **Goldhill** & **House** & **Lake** & **Peppers** \\ \hline No attack & 45.1236 & 46.2937 & 45.9640 & 45.4352 & 45.6023 & 45.6903 \\ Salt and pepper noise (m = 0, v = 0.05) & 21.9930 & 18.1367 & 19.5018 & 21.6362 & 22.5985 & 21.0464 \\ Gaussian noise (m = 0, v = 0.05) & 16.4985 & 14.8436 & 15.1894 & 15.7981 & 15.2616 & 14.9989 \\ Speckle noise (m = 0, v = 0.05) & 17.2991 & 15.6238 & 17.0665 & 18.8839 & 20.6056 & 18.9589 \\ Sharpening & 17.8137 & 11.7404 & 13.7391 & 12.2267 & 14.3804 & 16.0217 \\ Gaussian filter & 27.1655 & 17.4290 & 20.0078 & 23.2353 & 25.5899 & 27.6140 \\ Mean filtering (\(3\times 3\)) & 25.4989 & 16.6578 & 19.3077 & 21.6643 & 23.9667 & 25.8653 \\ Rotation (\(10^{\circ}\)) & 12.5688 & 11.9637 & 8.9287 & 7.3895 & 10.9374 & 9.4181 \\ Flip vertical & 45.1236 & 46.2937 & 45.9640 & 45.4352 & 45.6023 & 45.6903 \\ Cropping (\(20\%\)) & 15.1805 & 12.4529 & 16.8821 & 11.9011 & 10.4191 & 12.3544 \\ JPEG (QF = 90) & 40.3817 & 29.1525 & 23.3808 & 35.2028 & 32.7321 & 37.1544 \\ JPEG2000 (QF = 90) & 31.1487 & 18.6613 & 19.7050 & 25.8294 & 28.2891 & 30.7598 \\ \hline \end{tabular}
\end{table} 
Table 4: PSNR of watermark image extracted from different attacks. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Type of Attack** & **Airplane** & **Baboon** & **Goldhill** & **House** & **Lake** & **Peppers** \\ \hline No attack & 45.3999 & 46.1830 & 46.3581 & 45.7942 & 46.0233 & 45.8709 \\ Salt and pepper noise (m = 0, v = 0.05) & 24.1925 & 24.5199 & 24.2839 & 24.2808 & 24.0658 & 24.0156 \\ Gaussian noise (m = 0, v = 0.05) & 21.9604 & 21.1743 & 21.3477 & 21.5720 & 21.6848 & 21.3546 \\ Speckle noise (m = 0, v = 0.05) & 23.3501 & 24.2688 & 25.1576 & 23.4628 & 24.6759 & 24.1880 \\ Sharpening & 22.7583 & 14.5942 & 21.5463 & 21.0908 & 20.0830 & 22.1108 \\ Gaussian filter & 26.6688 & 23.8386 & 26.5525 & 26.2767 & 26.2735 & 26.7413 \\ Mean filtering (\(3\times 3\)) & 26.3346 & 22.9468 & 26.1975 & 25.8654 & 25.9057 & 26.5179 \\ Rotation (\(10^{\circ}\)) & 11.7224 & 13.8714 & 13.6429 & 11.9677 & 11.8750 & 12.4293 \\ Flip vertical & 13.3158 & 13.7236 & 11.6019 & 13.3698 & 10.6806 & 11.3423 \\ Cropping (\(20\%\)) & 17.9468 & 18.7958 & 20.9153 & 18.5873 & 18.6055 & 19.2897 \\ JPEG (QF = 90) & 27.1407 & 27.2344 & 27.1477 & 27.1401 & 27.0337 & 27.1295 \\ JPEG2000 (QF = 90) & 26.1510 & 22.5929 & 25.8521 & 25.3871 & 25.0508 & 26.2070 \\ \hline \end{tabular}
\end{table} 
Table 3: PSNR of the attacked watermark cover image. \begin{table}
\begin{tabular}{l c c c c c} \hline
**Type of Attack** & **Airplane** & **Baboon** & **Goldhill** & **House** & **Lake** & **Peppers** \\ \hline No attack & 1 & 1 & 1 & 1 & 1 \\ Salt and pepper noise (m = 0, v = 0.05) & 0.9918 & 0.9971 & 0.9918 & 0.9953 & 0.9962 & 0.9948 \\ Gaussian noise (m = 0, v = 0.05) & 0.9146 & 0.9242 & 0.9060 & 0.9193 & 0.9246 & 0.9062 \\ Speckle noise (m = 0, v = 0.05) & 0.9822 & 0.9947 & 0.9917 & 0.9915 & 0.9966 & 0.9976 \\ Sharpening & 0.9745 & 0.8958 & 0.9562 & 0.9571 & 0.9402 & 0.9694 \\ Gaussian filter & 0.9960 & 0.9575 & 0.9928 & 0.9893 & 0.9887 & 0.9959 \\ Mean filtering (\(3\times 3\)) & 0.9944 & 0.9435 & 0.9898 & 0.9902 & 0.9839 & 0.9942 \\ Rotation (\(10^{\circ}\)) & 0.8182 & 0.8715 & 0.8379 & 0.8332 & 0.8844 & 0.9742 \\ Flip vertical & 1 & 1 & 1 & 1 & 1 & 1 \\ Cropping (\(20\%\)) & 0.8871 & 0.9636 & 0.9817 & 0.9613 & 0.9009 & 0.9848 \\ JPEG (QF = 90) & 0.9986 & 0.9966 & 0.9992 & 0.9999 & 0.9995 & 0.9999 \\ JPEG2000 (QF = 90) & 0.9983 & 0.9611 & 0.9951 & 0.9967 & 0.9918 & 0.9983 \\ \hline \end{tabular}
\end{table} 
Table 5: NCC of watermark image extracted from different attacks.