Quaternion image watermarking using the spatio-chromatic fourier coefficients analysis

Abstract

In this paper, a new color watermarking algorithm that uses the quaternion fourier transform (QFT) to mark the La * b * components of color images is presented. First, we propose an interpretation of the QFT coefficients using the SpatioChromatic Fourier analysis, so the effects of any changes to the coefficients can be predicted. Next, watermark casting is performed by modifying the positive and negative coefficients together. The idea is twofold: Robustness is achieved by embedding a color watermark in the coefficient with positive frequency, which spreads it to all components in the spatial domain. On the other hand, invisibility is satisfied by modifying the coefficient with negative frequency, such that the combined effects of the two are insensitive to human eyes.

Optimal and secure audio watermarking scheme based on self-adaptive particle swarm optimization and quaternion wavelet transform

“…From Table 9, we observed that our proposed QWT-SVD-SAPSO algorithm achieves relatively higher capacity and imperceptibility. Higher SNR results are obtained in our proposed scheme compared with those in [16][17][18][19][20][21][22]. Among the selected SVDrelated algorithms, the QWT-SVD-SAPSO algorithm is the highest in terms of SNR and SDG values, which demonstrates good imperceptibility of the proposed scheme.…”

“…The typical audio watermarking schemes with and without SVD transform are selected for this comparison. Table 9 shows the comparison results of the selected SVD-related audio watermarking schemes [16][17][18][19][20][21][22] regarding robustness, imperceptibility, capacity, and other characteristics. From Table 9, we observed that our proposed QWT-SVD-SAPSO algorithm achieves relatively higher capacity and imperceptibility.…”

“…In [17], the full 4D QFT had been proposed to address general color image watermarking problems by introducing symmetrical constraints and solving the energy loss issue. In [18], Tsui proposed a non-blind algorithm to embed bit sequence into host signal by QFT. The patterns are modulated to insert the watermark into the QFT coefficients.…”

Full 4-D quaternion discrete Fourier transform based watermarking for color images

“…Quaternions, which have been more and more used in color imagep rocessing in the past two decades, offer an interesting solution to achieve this goal. They represent an image by encoding its three color channels on the imaginary parts of quaternion numbers [4][5][6][7][8][9][10][11][12][13][14][15][16]. The main advantage of such a representation is that a color image can be processed holistically as a vector field [5][6][7].S o does color image watermarking [8][9][10][11][12][13][14][15][16], which mainly makes use of the quaternion discrete Fourier transform (QDFT).…”

Novel gray-scale watermarking algorithm based on QFT

“…In [5], T.K.Tsui proposed a new quaternion based watermarking. It interprets the QFT coefficients using spatio-chromatic Fourier analysis and robustness and invisibility is balanced by modifying both positive and negative coefficients.…”