# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 5 Experiments and Results
### Watermarking Robustness against Attacks
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Attack/(Parameter)** & **Value Range (Step)** & **MSE** & **PSNR (dB)** & **NCC** & **SSIM** & **MSSIM** & **B\({}_{error}\)** & **BER** \\ \hline Gaussian Filter/(\(N\times N\)) & 2 to 11 (1) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline Median Filter/(\(N\times N\)) & 2 to 9 (1) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline Gaussian Noise/(\(\sigma^{2}\)) & 0.05 to 0.5 (0.05) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline Salt and Pepper Noise/(density) & 0.1 to 1 (0.1) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline Scaling/(scale factor) & 0.25 to 4 (0.25) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline Translation/(pixels) & 10 to 100 (10) & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline \multirow{9}{*}{Rotation/(angle \({}^{\circ}\))} & 1 & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\  & 15 & 4564.7550 & 11.5366 & 0.8201 & 0.4416 & 0.4326 & 147 & 0.0366 \\  & 30 & 7601.4225 & 9.3219 & 0.7321 & 0.3890 & 0.3843 & 261 & 0.0650 \\  & 45 & 8908.4250 & 8.6328 & 0.6992 & 0.3739 & 0.3699 & 327 & 0.0814 \\  & \(\gg\)60 & 7724.9700 & 9.2518 & 0.7289 & 0.3909 & 0.3863 & 299 & 0.0744 \\  & 75 & 4493.2275 & 11.6052 & 0.8224 & 0.4436 & 0.4342 & 172 & 0.0428 \\  & 90 & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\  & 105 & 4564.7550 & 11.5366 & 0.8201 & 0.4416 & 0.4326 & 147 & 0.0366 \\  & 120 & 7601.4225 & 9.3219 & 0.7321 & 0.3890 & 0.3843 & 261 & 0.0650 \\  & 135 & 8908.4250 & 8.6328 & 0.6992 & 0.3739 & 0.3699 & 327 & 0.0814 \\  & 150 & 7724.9700 & 9.2518 & 0.7289 & 0.3909 & 0.3863 & 299 & 0.0744 \\  & 165 & 4493.2275 & 11.6052 & 0.8224 & 0.4436 & 0.4342 & 172 & 0.0428 \\  & 180 & 0 & \(\gg\)60 & 1 & 1 & 1 & 0 & 0 \\ \hline \multirow{9}{*}{Cropping/(\(p\) %)} & 5 & 1703.6550 & 15.8170 & 0.9239 & 0.5595 & 0.5079 & 28 & 0.0070 \\  & 10 & 3290.2650 & 12.9585 & 0.8633 & 0.4735 & 0.4589 & 62 & 0.0154 \\  & 15 & 5806.7325 & 10.4915 & 0.7819 & 0.4225 & 0.4165 & 109 & 0.0271 \\  & 20 & 8973.4500 & 8.6012 & 0.6977 & 0.3772 & 0.3734 & 226 & 0.0562 \\  & 25 & 11,724.0075 & 7.4400 & 0.6361 & 0.3456 & 0.3425 & 342 & 0.0851 \\  & 30 & 14,741.1675 & 6.4455 & 0.5775 & 0.3133 & 0.3107 & 475 & 0.1182 \\  & 35 & 18,011.9250 & 5.5752 & 0.5216 & 0.2777 & 0.2754 & 585 & 0.1456 \\  & 40 & 20,840.5125 & 4.9417 & 0.4781 & 0.2475 & 0.2453 & 701 & 0.1745 \\  & 45 & 23,974.7175 & 4.3333 & 0.4338 & 0.2166 & 0.2146 & 829 & 0.2063 \\ Cropping/(\(p\) %) & 50 & 27167.4450 & 3.7903 & 0.3919 & 0.1863 & 0.1844 & 967 & 0.2407 \\  & 55 & 29,989.5300 & 3.3611 & 0.3568 & 0.1589 & 0.1571 & 1082 & 0.2693 \\  & 60 & 33,370.8300 & 2.8971 & 0.3163 & 0.1278 & 0.1260 & 1239 & 0.3084 \\  & 65 & 35,991.3375 & 2.5688 & 0.2855 & 0.1042 & 0.1025 & 1348 & 0.3355 \\  & 70 & 37,766.5200 & 2.3597 & 0.2647 & 0.0892 & 0.0875 & 1420 & 0.3534 \\  & 75 & 40,159.4400 & 2.0929 & 0.2363 & 0.0707 & 0.0691 & 1518 & 0.3778 \\  & 80 & 42,772.9275 & 1.8237 & 0.2048 & 0.0473 & 0.0458 & 1637 & 0.4074 \\  & 85 & 44,685.1800 & 1.6292 & 0.1793 & 0.0341 & 0.0327 & 1716 & 0.4271 \\  & 90 & 47,214.6525 & 1.3900 & 0.1431 & 0.0188 & 0.0175