# Image Watermarking between Conventional and Learning-Based Techniques: A Literature Review
## 4 Conventional Image Watermarking Schemes
### Transform Domain
#### 4.2.2 Discrete Fourier Transform (DFT)  
In the Fourier domain, the image is decomposed into a sum of elementary signals in the form of complex periodic Fourier coefficients and represented as amplitude and phase. DFT properties allow the watermarking scheme to handle most geometrical distortions. Therefore, several DFT-based image watermarking approaches have been proposed. Firstly, [PERSON] et al. [87] came up with a frequency watermarking technique based on DFT and compressive sensing (CS) to increase the quality of the recovered image. This method is based on separable data hiding in encrypted images. In the first step, the selected coefficient matrices are generated from the DFT cover image; then, they are divided into the most significant information used for encryption, while other information is used for embedding. The scheme demonstrated excellent recovery and provided a flexible payload. However, there is still a need to realize fully reversible data hiding. Moreover, CS algorithms are time consuming, which reduces the chances of adopting this global watermarking method in real-world applications. In [88; 89], the authors proposed a DFT-based robust watermarking method for printed and scanned ID images. The watermark is circularly embedded within the DFT coefficient'smagnitude. In this context, two mechanisms have been associated with DFT-based image watermarking. A Wiener filter is used to reduce image blurring, while color correction is used to attenuate color degradations. The whole scheme has good resistance to geometric attacks produced by the print-scan process, and it shows high efficiency and low computational cost. Further, [PERSON] et al. [90] improved the previous watermarking scheme for the print-cam process by including a pre-processing stage to correct the perspective deformations using the Hough line transform. Accordingly, enhanced robustness against the strong geometric attacks produced by the print-cam process. On the other hand, [PERSON] et al. [91] introduced a non-blind and Fourier-based image watermarking scheme. A bulk watermark is generated, then the DFT is applied to the cover image. Following that, a progressive division is applied to the bulk watermark in order to scale down the intensity of each pixel. To retrieve the watermark, the DFT watermarked image and DFT host image are subjected to a detection process based on successive multiplication processes. Better imperceptibility is observed in the results with less execution time. The algorithm provides the same data capacity as other algorithms studied in this work, and DWT can be used to increase data-embedding capacity. Likewise in [92], various variants of the Fourier transform were used (e.g., discrete Fourier transform, a fractional Fourier transform, as well as a quaternion discrete Fourier transform) to conceal the watermark in the medium-frequency band of the original image. According to the results, the system performs well against filtering attacks and produces high-quality watermarked images. However, the embedding scheme requires three coefficients to insert two bits, significantly reducing the capacity of the watermarking method. [PERSON] et al. [93] exploited DFT-based watermarking embedding to cope with perspective distortions produced by the screen-cam process. For this purpose, the watermark is concealed in the middle-frequency DFT coefficients, which are quite resilient to changes in media data. At the extraction phase, a synchronization mechanism is used to rectify the perspective transformations. Finally, the watermark is extracted using a message extraction algorithm based on the local maximum value from the DFT of the noise component. This method shows robustness to common attacks, as well as screen-cam attacks. Although perspective correction will never be perfect, the correction must enhance the effectiveness of the automatic perspective correction approach so that it may be employed in real-time copyright verification applications. Furthermore, the watermark capacity should be increased.