Color Image Watermarking Using Multidimensional Fourier Transforms

This paper 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 frequency domain that is consistent with our human visual system. Watermark casting is performed by estimating the just-noticeable distortion of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image into the CIE chromaticity coordinates while the achromatic content is encoded as CIE tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using the spatiochromatic discrete Fourier transform. It first encodes and 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 components of color images and watermarks are embedded as vectors in the frequency domain of the channels by using the quaternion Fourier transform. Robustness is achieved by embedding a watermark in the coefficient with positive frequency, which spreads it to all color components in the spatial domain and invisibility is satisfied by modifying the coefficient with negative frequency, such that the combined effects of the two are insensitive to human eyes. Experimental results demonstrate that the two proposed algorithms perform better than two existing algorithms - ac- and discrete cosine transform-based schemes.