Hybrid Watermarking Algorithm Using Clifford Algebra With Arnold Scrambling and Chaotic Encryption

Abstract

With the widespread use of color images, the copyright protection of those images using watermarks is one of the latest research topics. The use of color images as watermarks has advantages over binary and irreplaceable grayscale images. Color images are intuitive, rich, and lively; they have large amounts of copyright protection information and more easily recognized by human vision. To improve the security of watermark information and embedding positions and improve the algorithm's robustness against various attacks, a Quaternion Fourier transform (QFT) based algorithm, based on Arnold transform and chaotic encryption, is proposed in this paper. Geometric algebra (GA) can deal with color images in vector form with each component of RGB handled individually. We used Quaternion, which is a sub-algebra of GA, and effectively handled color image processing by using Fourier transformation. After deriving the calculation process of the QFT with strong security by Arnold scrambling and chaotic encryption, this paper proposes a digital watermarking algorithm that resists geometric attacks by using color images as carriers. The robustness and quality of the proposed watermarking algorithm is tested with different with many statistical measures. Experimental outcomes show that the proposed approach is the best to solve conflict problems between quality and robustness. Also, the proposed approach exhibits worthy robustness against many attacks, such as, conventional attacks, and geometrical attacks.INDEX TERMS QFT, Arnold scrambling, chaotic encryption, Clifford algebra.

Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

“…Affes et al [23] designed a CFT content-based watermark, which employs the Harris detector to find the area of interest, then uses the CFT to embed it in the frequency of the image. In our other work [1], we used the quaternion Fourier transform (QFT) to watermark color images as RGB components are perfectly handled in quaternion-based CA. Hsu et al [24] used quaternion the discrete Fourier transform (QDFT) via the modulation technique, while Hosney et al [24] used quaternion Legendre-Fourier moments (QLFMs) to embed a watermark in polar coordinates.…”

“…Geometric algebra (GA) provide a unified and concise homogeneous algebra framework based on advanced geometric invariants, projection geometry, affine geometry, etc., [1], [30]. It can efficiently solve the geospatial data processing problems described above due to its advanced geometrical vector-based data processing.…”

Clifford Geometric Algebra-Based Approach for 3D Modeling of Agricultural Images Acquired by UAVs

“…Where q R (x, y), q G (x, y),and q B(x,y) represents pixel values of red,green and blue respectively. The x and y here represent position of the specific pixel on x and y coordinates [33]. In geometric algebra, a rotor R, is an even-grade element of algebra which satisfies RR = 1, whereR stands for conjugate of R.…”

New watermarking algorithm utilizing quaternion Fourier transform with advanced scrambling and secure encryption

“…The red, green and blue colors can be overlaid for further colors. Because of the 256 brightness levels of these three primary colors, 16.7 million colors are superimposed [1]. A two-dimensional matrix by sampling will discretize the continuous image into a digital image.…”

“…& Single-channel method: According to the human eye's characteristic of being insensitive to changes in the blue component in the RGB color model, by modifying the blue component value of the color image or transforming it to the transform domain, embed watermark information in the transform domain; [16,31,33] or Convert the color image from the RGB color model to the YUV or YCbCr color model, and then embed a watermark in the [1,14,30]. Although this type of algorithm can extend the watermark to the entire image, it still separates the components of the pixel, and does not consider the relationship between the components of the pixel, and the algorithm needs to transform and embed each component of the color image.…”