# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 6 Discussion
element to take into account is the scaling factor \(\alpha\) because it defines the imperceptibility and robustness of the watermarking method. Both insertion and extraction processes were similar. Therefore, the proposed method is symmetric, and the extraction stage applied the inverse operations to those used in the insertion. To probe the effectiveness of this method, we applied the insertion and extraction process to 49 different digital images, evaluated its robustness against attacks, and compared it with other methods. To probe the quality of our algorithm, we used typical metrics employed in this kind of application (MSE, PSNR, SSIM, MSSIM, NCC, and BER). For the original image, the watermarked image, the original watermark (LOGO), and the extracted watermark, we employed the metrics that indicated if an image had suffered visual alterations or if two images were equal, and in the case of the MetaData, we calculated the BER to measure how many bits were modified in the recovered watermark. The metrics' values of Table 2 demonstrated that the watermarked images did not have visual modifications and the extracted watermarks (LOGO and MetaData) were the same as the originals. Furthermore, we presented the results of six representative images (Table 3). In all cases, the extracted watermark (LOGO) and MetaData were equal to the original. The watermarked image did not have visual modifications, although the worst MSE was obtained with the _Cameraman_ image (MSE = 9.9479). Therefore, this algorithm guarantees imperceptibility and perfect extraction. To evaluate the algorithm regarding the robustness, we probed it with the majority of attacks that are common in watermark applications. In total, we applied 11 attacks (common processing and geometrics). From Table 4, we can see that, for four attacks, _Gaussian noise_, _SP noise_, _scaling_, and _contrast enhancement_, the watermark could be recovered perfectly without errors, while for the rest of the attacks, the metrics' values indicated that the extracted watermark could have some difference in comparison with the watermarked original. However, this difference did not prevent the identification of the LOGO; however, it was clear that the modification of the bits in the MetaData did change its meaning. However, if one of the two watermarks is clear, we can validate the method. The worst cases to recover the watermark were when we applied the _cropping_ and _rotation_ attacks. Finally, in comparison with other similar algorithms, it is clear that our proposal presented equal or higher values for all metrics (Table 6). It is important to note that it was difficult to compare with other proposals because, in some cases, we used stronger attacks. Therefore, we presented the outcomes of the algorithms employing identical parameters to ours (Tables 8-14). Is clear that our method had better robustness and watermark capacity. Another difficulty was comparing with other methods, but using different images, because this depended on the published results for each research work. Therefore, from the state-of-the-art evaluation, we could select some of them that presented tests using different images from the _Lena_ image.