# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 5 Experiments and Results
### Watermarking Robustness against Attacks  
To evaluate the robustness against attacks of the proposed watermarking method, we applied the most-common processing and geometric attacks to the 49 grayscale watermarked images of Section 3.1. _Processing operations:_ Gaussian filter and median filter; Gaussian noise and salt and pepper noise. _Gaussian filter_--window of \(N\times N\) and varying \(N\) from 2 to 11; _median filter_--window of \(N\times N\), and \(N\) varies between 2 and 9; _Gaussian noise_--with \(\sigma^{2}\in[0,0.5]\) and increments of 0.05; _SP noise_--with noise density varying between 0 and 1 and increments of 0.1. Additionally, we applied image compression and image scaling. _JPEG compression_--with a variation of the quality factor between 0% and 100% and steps of 10%; _Scale_--with a scale varying between 0.25 and 4 and steps of 0.25. Furthermore, we applied histogram equalization and contrast enhancement. _Equalization_--varying the discrete equalization levels \(2^{n}\), where \(n\) is from 2 to 8. _Contrast enhancement_--varying \(f\) from 0.01 to 0.45 with increments of 0.05, such as suturing the bottom \(f\%\) and the top \((1-f\%)\) of all pixel values using the histogram information. _Geometric attacks: Rotation_--varying the rotation angle from \(1^{\circ}\) to \(180^{\circ}\) with steps of \(5^{\circ}\). _Translation_--the variation was from 10 to 100 px, with increments of 10. Finally, we _cropped_ the watermark image, substituting the original pixels for black pixels. In percentage \(p\) was from 0 to 95%. Table 4 shows the metrics' averages using the 49 grayscale watermarked images for all attacks with parameter variation, including the metrics of the LOGO and MetaData recovered. As we can see, only with the _Rotation_ and the _Cropping_ was it difficult to recover the LOGO and the MetaData. For both cases, the bits modified in the MetaData were significant, and the LOGO images had visual modifications because the PSNR values and the SSIM values were high. With _Gaussian noise, SP noise, scale_, and _contrast enhancement_, \(BER=0\), \(PSNR\gg 60\), NCC = 1, SSIM = 1, MSSIM = 1, and MSE = 0, indicating that the recovered watermark was equal to the inserted watermark. In the rest of the attacks (_Gaussian filter, median filter, translation, JPEG compression_, and _histogram equalization_), the values of the PSNR, NCC, SSIM, and MSSIM indicated that there was a high similarity between the original watermark and the extracted watermark. In the case of the LOGO image, it could present visual changes, but it was still visible, and the MetaData changed in some characters. It is important to note that, in this table, we included the \(BER\) (number of modified bits) and \(B_{error}\) (BER ratio) to identify if a LOGO had modified bits. For example, with the Gaussian filter, \(BER=0\) indicates that the watermark did not have modified bits, but if we calculated the BER ratio (\(B_{error}\)), it was clear that it had few modifications. To analyze in detail the results of the robustness against attacks, in Table 5, we show the metrics' averages for all attacks with parameter variation, showing the metrics for the recovery of the LOGO and MetaData extracted after applying the algorithm using only the _Lena_ image. The results for each metric demonstrated that our proposal is robust and imperceptible. In Figure 14-16, we present the original _Lena_ image, recovered watermark, and recovery MetaData after applying some attacks. In Figure 14, we can observe that, after applying the median filter, SP noise, and JPEG compression, it was possible to recover the watermark and MetaData. The same result was obtained if we applied histogram equalization and translation (Figure 15). Finally, in Figure 16, we can see that, if we rotate or crop the watermark image, in some cases, it was not possible to recover the watermark and the MetaData without modifications, but in the majority of the cases, we had good results.