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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.

In this paper, a color watermarking algorithm is proposed. The method encodes the chromatic content of a color image as CIE a * b * chromaticity coordinates whereas the achromatic content is encoded as CIE L tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using the Spatio Chromatic Discrete Fourier Transform (SCDFT). It first encodes a * and b * as complex values, followed by a single discrete Fourier Transform. Watermark casting is performed by estimating the Just-Noticeable distortion (JND) of the images, to ensure watermark invisibility. The most interesting characteristics of the new scheme is the possibility of performing watermarking in the frequency domain of chromatic components.

This thesis presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the coefficients consistent with our human visual systems (HVS). Watermark casting is performed by estimating the Just-Noticeable distortion (JND) of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image as CIE a*b* chromaticity coordinates whereas the achromatic content is encoded as CIE L tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using Spatio Chromatic Discrete Fourier Transform (SCDFT). It first encodes a* and b* as complex values, followed by a single discrete Fourier Transform. The most interesting characteristic of the scheme is the possibility of performing watermarking in the frequency domain of chromatic components. The second method encodes the L*a*b* components of color images and color watermarks are embedded as vectors in the frequency domain of the channels by using the Quaternion Fourier Transform (QFT). 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

This thesis presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the coefficients consistent with our human visual systems (HVS). Watermark casting is performed by estimating the Just-Noticeable distortion (JND) of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image as CIE a*b* chromaticity coordinates whereas the achromatic content is encoded as CIE L tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using Spatio Chromatic Discrete Fourier Transform (SCDFT). It first encodes a* and b* as complex values, followed by a single discrete Fourier Transform. The most interesting characteristic of the scheme is the possibility of performing watermarking in the frequency domain of chromatic components. The second method encodes the L*a*b* components of color images and color watermarks are embedded as vectors in the frequency domain of the channels by using the Quaternion Fourier Transform (QFT). 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