Discrete orthogonal polynomials are useful tools in digital image processing to extract vi-sual object contours in different application contexts. This paper proposes an alternative method that extends beyond classic first-order differential operators, by using the prop-erties of Krawtchouk orthogonal polynomials to achieve a first order differential operator. Therefore, smoothing of the image with a 2-D Gaussian filter is not necessary to regularize the ill-posed nature of differentiation. Experimentally, we provide simulation results which show that the proposed method achieves good performance in comparison with commonly used algorithms.

Let P (α,β ) n be the n-th monic Jacobi polynomial with α, β > −1. Given m numbersnormalized by the conditionsThe main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of monic polynomials {P (α,β )n,m,Ω m } n . In particular, we obtain the relative asymptotic for the ratio of the sequences {P (α,β ) n,m,Ω m } n and {P (α,β ) n } n . We prove that the zeros of these polynomials accumulate on a suitable ellipse.

We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein-Chen-Dilcher's polynomials play an important role in this issue. For these polynomials we find their strong asymptotics and give the limit measure of their zero distribution. We apply these results to describe the zero asymptotic distribution of iterated integrals of ultraspherical polynomials with parameters (2α + 1)/2, α ∈ Z+.

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We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein-Chen-Dilcher's polynomials play an important role in this issue. For these polynomials we find their strong asymptotics and give the limit measure of their zero distribution. We apply these results to describe the zero asymptotic distribution of iterated integrals of ultraspherical polynomials with parameters (2α + 1)/2, α ∈ Z + .