Estimation of Data Hiding Capacities in Spatio-Chromatic Fourier Transform (SCFT) Representations of Color Images

Despite the abundance of color images, a vast majority of digital image watermarking algorithms are specifically designed for gray-scale images in terms of perceptual modeling, watermark embedding and data hiding capacity. This paper tries to bridge this gap and provides information theoretic estimates of data hiding capacities for standard color images using an improved version of the CIEL*a*b* color space. These capacity estimates are derived based on appropriate color models of the spatio-chromatic Fourier transform (SCFT) of the host image, distortion constraints imposed on the watermarking game players (watermark embedder and attacker), and side information available to both players. This paper considers full-frame and block-based SCFT statistical representations for color images and derive data hiding bounds for these image sources assuming invariance to affine and geometric attacks. Finally, the estimated data hiding capacities are used to assess the performance of a color-based SCFT image watermarking algorithm. The performance results highlight the importance of combining the estimated hiding capacities and perceptual model in designing a high capacity, robust and perceptual color image watermarking system.