# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 5 Experiments and Results
### Comparison with other Methods  
In order to evaluate our proposed scheme, we compared it to other similar approaches. To have a valid comparison, it is important to have elements in common, such as the database, watermark type, the metrics to evaluate each algorithm, and the attacks applied. After reviewing the state-of-the-art, we decided to compare our algorithm to algorithms that use typical images for this application (_Baboon_, _Barbara_, _Boat_, _Cameraman_, _Lena_, and _Peppers_)and at least used as metrics the PSNR, SSIM, and 2D correlation. Implementing the algorithms that we selected to compare our method was difficult because, in some cases, the authors did not include their proposals with details, so we took their published results. In Table 6, we present the results of our proposal compared with [1, 5, 6, 9, 13, 17, 29, 31, 32, 33, 34, 35]. In all cases, the original image used was _Lena_. The metrics shown are of the watermarked image. As we can see from Table 6, the proposals reported good results for all metrics, including ours, but a small difference implies better development. Concerning the PSNRs, even though [29] reported the highest PSNR value, success against attacks was not guaranteed. Furthermore, we can assume that, when two images are equal, their \(\text{PSNR}=60\) dB, so any algorithm that reported PSNR values \(=60\) or \(\gg\)60 indicated that both the watermarked and the original image were equal. In this situation, our algorithm and the algorithms [6, 29, 31, 32] had PSNR values \(\gg\)60. Regarding the SSIM and NCC, the best results were obtained by our proposal and [6, 29, 35], so we can assume that the watermark image did not have perceptual modifications. Finally, with our algorithm, there was no error (\(\text{MSE}=0\)) between the original and the marked image. Only two techniques [32, 35] reported MSE values, and they were different from zero. Therefore, our method did not have errors in the insertion process and extraction process. Finally, after reviewing each result of [6, 29] and our proposal, the three methods had the same values for the SSIM and NNC, in addition to reported values of PSNR \(=\gg\)60 dB; there was no difference between them, so we can conclude that the three methods are good watermarking techniques. However, there was a difference between them: the watermark. In [29], the authors used an image (\(256\times 256\)); in [6], they used a LOGO (\(64\times 64\)); with our proposal, it is possible to insert both an image (\(100\times 100\)) and information about the owner or the technical data of the \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Method** & **Type of Watermark** & **PSNR (dB)** & **SSIM** & **NCC** & **MSE** \\ \hline
**Proposal** & Logo (\(100\times 100\)) and MetaData & \(\gg\)**60** & **1** & **1** & **0** \\ \hline [PERSON] et al. [31] & Grayscale Image & 57.6300 & 0.9984 & - & - \\ \hline [PERSON] et al. [29] & Grayscale Image (\(256\times 256\)) & 291.4853 & **1** & **1** & - \\ \hline [PERSON] et al. [32] & Logo & 73.7205 & 0.9884 & 0.9999 & 1.0827 \(\times\)\(10^{-5}\) \\ \hline [PERSON] et al. [1] & Signature (Biometric Image \(256\times 256\)) & 39.4843 & 0.9964 & - & - \\ \hline [PERSON] et al. [5] & Grayscale Image (\(64\times 64\)) & 41.7050 & - & **1** & - \\ \hline [PERSON] et al. [6] & Copyright Logo (\(64\times 64\)) & 74.4037 & **1** & **1** & - \\ \hline [PERSON] et al. [33] & Grayscale Image (\(32\times 32\)) & - & 0.9979 & 0.9956 & - \\ \hline [PERSON] et al. [9] & Grayscale Image (\(64\times 64\)) & 53.9470 & - & **1** & - \\ \hline [PERSON] et al. [13] & Grayscale Image (\(256\times 256\)) & 30 & 0.9938 & 0.9965 & - \\ \hline [PERSON] et al. [17] & Binary Logo (\(32\times 32\)) & 40 & 0.9720 & - & - \\ \hline [PERSON] et al. [35] & Logo (\(512\times 512\)) & 48.1308 & **1** & **1** & 1 \\ \hline [PERSON] et al. [34] & Image (\(32\times 32\)) & 46.3805 & 0.9979 & 0.9956 & - \\ \hline \hline \end{tabular}
\end{table}