# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 5 Experiments and Results
### Comparison with other Methods
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Proposal**} & \multicolumn{4}{c}{**[PERSON] et al. [13]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} & \multicolumn{4}{c}{**[PERSON] et al. [31]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} \\ \cline{2-13}
**Windew Size** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** \\ \hline
30\({}^{\circ}\) & 0.0567 & 9.3219 & 0.3890 & 0.7321 & - & - & - & - & 0.9988 & - & - & 8.6942 & 0.3322 & 0.8279 \\ \hline
60\({}^{\circ}\) & 0.0582 & 9.2518 & 0.3909 & 0.7289 & - & - & - & - & 0.9988 & - & 8.5953 & 0.3187 & 0.8244 \\ \hline
90\({}^{\circ}\) & **0** & **\(\gg\)**0** & **1** & **1** & - & - & **1** & - & - & **1** & - & 291.7367 & **1** & **1** \\ \hline
120\({}^{\circ}\) & 0.0612 & 9.3219 & 0.3890 & 0.7320 & - & - & - & 0.9988 & - & - & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparison between different types of watermarking systems [29; 31] with our algorithm, after applying the rotation attack using the _Lena_ image. The best result for each parameter is indicated by the values highlighted in bold in each column. \begin{table} \begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Proposal**} & \multicolumn{4}{c}{**[PERSON] et al. [31]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} & \multicolumn{4}{c}{**[PERSON] et al. [29]**} \\ \cline{2-13}
**Windew Size** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** & **BER** & **PSNR (dB)** & **SSIM** & **NCC** \\ \hline
**(2 \(\times\) 2  
Regarding Gaussian noise, only the algorithm from [34] used the same parameter of the noise density to probe their proposal as ours. In Table 13, we can see the results. Meanwhile, in Table 14, we present the results of SP noise compared with [13; 34].  
From the results shown in Tables 13 and 14, we can confirm that, when we applied Gaussian noise or SP noise to the marked image, we could fully extract the watermarks. The metrics' values for SSIM and NCC were equal to \(1\) using our algorithm, and BER = 0.  
Finally, we decided to include a comparison with other techniques using different images. The comparison of Gaussian noise with [33] is presented in Table 15 using the _Barbara_ image. Table 16 shows the metrics' values after applying SP noise compared with [34], using the _Pirate_image, and Table 17 presents the comparison of JPEG compression, using the _Baboon_ image, with [17; 34].  
As we can see from Tables 15-17, we demonstrated with our method that it is possible to extract the watermark without errors even using different images, not only the _Lena_ image.  
\begin{table}
\begin{tabular}{c} **PSNR** \\ **(dB)** \\ \end{tabular} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{NCC} \\ \hline
0.1 & **0** & \(\mathbf{\gg}\)**60** & **1** & **1** & - & - & 0.9067 & 0.9241 \\ \hline
0.3 & **0** & \(\mathbf{\gg}\)**60** & **1** & **1** & - & - & 0.8915 & 0.9279 \\ \hline
0.5 & **0** & \(\mathbf{\gg}\)**60** & **1** & **1** & - & - & 0.8808 & 0.9188 \\ \hline \hline \end{tabular} 
\end{table}
Table 13: Comparison between watermarking systems [34] with our algorithm, after applying Gaussian noise using the _Lena_ image. The best result for each parameter is indicated by the values highlighted in bold in each column.