Watermarking Applications of Krawtchouk–Sobolev Type Orthogonal Moments

Abstract

In this contribution, we consider the sequence {Hn(x;q)}n≥0 of monic polynomials orthogonal with respect to a Sobolev-type inner product involving forward difference operators For the first time in the literature, we apply the non-standard properties of {Hn(x;q)}n≥0 in a watermarking problem. Several differences are found in this watermarking application for the non-standard cases (when j>0) with respect to the standard classical Krawtchouk case λ=μ=0.

An Efficient Computation of Discrete Orthogonal Moments for Bio-Signals Reconstruction

“…Zhu et al [11,12] demonstrated that discrete orthogonal moments are more effective than continuous orthogonal moments at representing images. The types of discrete orthogonal moments (DOMs) according to their corresponding discrete orthogonal polynomials include Tchebichef [13,14], Krawtchouk [15][16][17][18], Charlier [19,20 ], Hahn [21,22] and Meixner [23,24] moments. At the present time, Discrete Orthogonal Moments (DOMs) are gaining popularity in analyzing one-dimensional signals due to their effectiveness in capturing digital information without redundancy.…”

An efficient computation of discrete orthogonal moments for bio-signals reconstruction

“…Zhu et al [14,15] demonstrated that discrete orthogonal moments are more effective than continuous orthogonal moments at representing images. The types of discrete orthogonal moments (DOMs) according to their corresponding discrete orthogonal polynomials include Tchebichef [16,17], Krawtchouk [18][19][20][21], Charlier [22][23][24], Hahn [25,26] and Meixner [27,28] moments. At the present time, Discrete Orthogonal Moments (DOMs) are gaining popularity in analyzing one-dimensional signals due to their effectiveness in capturing digital information without redundancy.…”