# A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
## 1 Introduction  
Currently, digital watermarking has become a way to embed information into an image and protect it from unauthorized access and manipulation. Depending on digital content such as video, image, audio, and text and the application, algorithms can be developed for authentication, material security, trademark protection, and the tracking of digital content. The objective is to insert a watermark (digital image or text) into the digital content.  
There are important requirements to take into account when a watermarking algorithm is designed: _imperceptibility_, _robustness_, _security_, _capacity_, and _computational cost_. It is difficult to have an algorithm that embraces all requirements due to robustness, which refers to the ability to withstand image distortions that may compromise the imperceptibility of the watermark. Because of that, different techniques have been developed in order to improve robustness without compromising the original content. The state-of-the-art suggests that these algorithms can be designed in the spatial, transform, or hybrid domain. Thus, the algorithms alter the marked pixels to embed the watermark in the intensity domain of the image. The advantage of this is low computational complexity; however, the image suffers visible alterations, and the algorithm does not possess robustness against geometric transformations. In the transform domain, the watermark is embedded within specific elements to ensure enhanced resilience. Furthermore, the transforms can be combined to have hybrid domain watermarking. These kinds of methods increase the performance of the watermarking technique.  
Therefore, in a watermarking image method, the watermark must be robust and imperceptible or perceptible, depending on the application. In this paper, we propose a hybrid, robust, and imperceptibility watermarking approach using the Hermite Transform (HT), Singular-Value Decomposition (SVD), the Human Vision System (HVS), and the Discrete Cosine Transform (DCT) to protect digital images. As watermarks, we used a digital image LOGO and image MetaData (with information about the original image or the owner), so we inserted two different digital contents into a digital image. The Hermite transform is based on the Gaussian function derivatives, and it incorporates human visual system properties, so it allows a perfect reconstruction of the image. To have more security, the LOGO is encrypted using the Jigsaw Transform (JST) before inserting. In addition, the indexes to decrypt the LOGO are secured using the Elementary Cellular Automaton (ECA), increasing the security of the proposal. In addition, the image MetaData are secured using a random sequence generator and the XOR operation. Finally, the Hamming error correcting code was applied to the image MetaData to reduce channel distortion.  
The rest of the paper is divided as follows: Section 2 presents the related work describing the image watermarking methods using the DCT and SVD techniques and other space-frequency decomposition methods similar to the HT. We describe all the elements used to design the watermark algorithm such as the public dataset, JST, SVD, HT, DCT, HVS, and Elementary Cellular Automata (ECA) in Section 3. Section 4 details the proposed watermarking algorithm for the insertion/extraction of the watermarks. In Section 5, we report the experiments and results obtained in the insertion and extraction stages of the watermarks, including the computational complexity of the algorithm. In addition, we report the robustness analysis of the proposed method against the most-common processing and geometric attacks using the public image datasets, and we compare the algorithm with other methods of the state-of-the-art. Section 6 includes an analysis of the achieved results in this study, along with a comparison to other related works. Finally, Section 7 presents the conclusions and future work.