A digital watermark is an invisible mark embedded in a digital image which may be used for Copyright Protection. This paper describes how Fourier-Mellin transform-based invariants can be used for digital image watermarking. The embedded marks are designed to be unaaected by any comb ination of rotation, scale and translation transformations. The original image is not required for extracting the...

A digital watermark is an invisible mark embedded in a digital image which may be used for Copyright Protection. This paper describes how Fourier-Mellin transform-based invariants can be used for digital image watermarking. The embedded marks are designed to be unaaected by any combination of rotation, scale and translation transformations. The original image is not required for extracting the ...

This article deals with the problem of testing the hypothesis that q p-variate normal distributions are independent and that their covariance matrices are equal. The exact null distribution of the likelihood ratio statistic when q = 2 is obtained using inverse Mellin transform and the definition of Meijer’s G-function. Results for p = 2, 3, 4 and 5 are given in computable series forms.

We present a number of new solutions to an integral equation arising in the limiting theory of Bellman–Harris processes. The argument proceeds via straightforward analysis of Mellin transforms. We also derive a criterion for the analyticity of the Laplace transform of the limiting distribution on Re(u) ≥ −c for some c > 0.

Words where each new letter (natural number) can never be too large, compared to the ones that were seen already, are enumerated. The letters follow the geometric distribution. Also, the maximal letter in such words is studied. The asymptotic answers involve small periodic oscillations. The methods include a chain of techniques: exponential generating function, Poisson generating function, Mell...

The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is investigated. Analytic continuation and mean square estimates of Zk(s) are discussed, as well as connections with power moments of |ζ( 1 2 +ix)|, with the special emphasis on the cases k = 1, 2.

The compound models of clutter statistics are found suitable to describe the nonstationary nature of radar backscattering from high-resolution observations. In this letter, we show that the properties of Mellin transform can be utilized to generate higher order moments of simple and compound models of clutter statistics in a compact manner.

We resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth’s recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth’s recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.

High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries, digital search trees, quadtrees, and d...

We consider Kemp’s q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of classical convergence properties. From the results about distributions, we deduce some new convergence results for (q-)Krawtchouk and q-Charlier polynomials. Besides...