# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 6 Discussion  
The experiments and results demonstrated that the image watermarking method based on SVD, the HVS, the HT, and the DCT is a robust and secure technique with the capacity to insert two different watermarks, the image LOGO and the image MetaData, in plaintext format containing information about the cover image or the image's owner. Compared with the majority of the state-of-the-art proposals, we had an advantage because they only used one watermark. The evaluation of the algorithm was presented by applying different attacks (processing and geometric operations), using two watermarks, inserting both at the same time, and 49 digital images. We used four different metrics to demonstrate that the watermarked images did not suffer visual alterations and that the watermark extracted, in the majority of cases, was recovered perfectly. To have an imperceptible and robust algorithm, our proposal is a hybrid approach because we used the Hermite Transform (HT), Singular-Value Decomposition (SVD), the Human Vision System (HVS), and the Discrete Cosine Transform (DCT), and to have major security, we encrypted the watermark. On the one hand, we encrypted the watermark (LOGO) by combining the Jigsaw transform and ECA. On the other hand, we applied a Hamming error-correcting code to the MetaData, to reduce channel distortion. The insertion process (Figure 10) shows all the elements we considered. First, we applied the HT to the original image, because this transform guarantees imperceptibility. We chose the low-frequency coefficient and divided it into blocks of size \(4\times 4\). Then, to determine the best regions (with more redundant information) to insert the watermark, we used a combination of entropy and edge entropy (HVS analysis). Figure 11b shows an example highlighting the most-suitable regions to insert the watermark. This HVS analysis was applied to each block, and then, we used the DCT (this transformation demonstrated greater effectiveness when applied to smaller block sizes). To insert the watermark, we used SVD because, as we explained, the SVD of a digital image in the majority of cases is rarely affected by various attacks. We inserted the watermark into \(S\) coefficients. Finally, we applied the IDCT, and the blocks were joined to calculate the inverse HT. An important \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Noise Density**} & \multicolumn{2}{c}{**Proposal**} & \multicolumn{2}{c}{**[PERSON] et al. [34]**} \\ \cline{2-4}  & **SSIM** & **NCC** & **SSIM** & **NCC** \\ \hline
0.1 & **1** & **1** & 0.9282 & 0.9577 \\ \hline
0.3 & **1** & **1** & 0.8904 & 0.9238 \\ \hline
0.5 & **1** & **1** & 0.8706 & 0.9065 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Comparison between watermarking systems [34] with our algorithm, after applying SP noise using the _Pirate_ 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} \hline \hline \multirow{2}{*}{**Quality Factor**} & \multicolumn{2}{c}{**Proposal**} & \multicolumn{2}{c}{**[PERSON] et al. [17]**} & \multicolumn{2}{c}{**[PERSON] et al. [34]**} \\ \cline{2-9}  & **BER** & **SSIM** & **NCC** & **BER** & **SSIM** & **NCC** & **BER** & **SSIM** & **NCC** \\ \hline
90 & **0** & **1** & **1** & - & - & - & - & 0.9973 & 0.9987 \\ \hline
70 & **0** & **1** & **1** & 0.0010 & - & 0.9993 & - & - & - \\ \hline
60 & **0** & **1** & **1** & - & - & - & - & 0.9843 & 0.9053 \\ \hline
50 & **0** & **1** & **1** & 0.0029 & - & 0.9980 & - & - & - \\ \hline
30 & **0** & **1** & **1** & 0.0078 & - & 0.9947 & - & 0.9365 & 0.7868 \\ \hline
10 & **0** & **1** & **1** & 0.1143 & - & 0.9195 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Comparison between different types of watermarking systems [17; 34] with our algorithm, after applying JPEG compression using the _Baboon_ image. The best result for each parameter is indicated by the values highlighted in bold in each column.