Tchebichef image watermarking along the edge using YCoCg-R color space for copyright protection

Easy creation and manipulation of digital images present the potential danger of counterfeiting and forgery. Watermarking technique which embeds a watermark into the images can be used to overcome these problems and to provide copyright protection. Digital image watermarking should meet requirements, e.g. maintain image quality, difficult to remove the watermark, quality of watermark extraction, and applicable. This research proposes Tchebichef watermarking along the edge based on YCoCg-R color space. The embedding region is selected by considering the human visual characteristics (HVC) entropy. The selected blocks with minimum of HVC entropy values are transformed by Tchebichef moments. The locations of C(0,1), C(1,0), C(0,2) and C(2,0) of the matrix moment are randomly embedded for each watermark bit. The proposed watermarking scheme produces a good imperceptibility by average SSIM value around 0.98. The watermark recovery has greater resistant after several types of attack than other schemes.

Relations between the orthogonal matrix polynomials on [a, b], Dyukarev-Stieltjes parameters, and Schur complements

We obtain explicit interrelations between new Dyukarev-Stieltjes matrix parameters and orthogonal matrix polynomials on a finite interval [a, b], as well as the Schur complements of the block Hankel matrices constructed through the moments of the truncated Hausdorff matrix moment (THMM) problem in the nondegenerate case. Extremal solutions of the THMM problem are described with the help of matrix continued fractions.