Volume 32 • Number 3 • 2009   • Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials S. L. Lee Abstract. The derivatives of the Gaussian function, , produce the Hermite polynomials by the relation, , where , are Hermite polynomials of degree . The orthonormal property of the Hermite polynomials, , can be considered as a biorthogonal relation between the derivatives of the Gaussian, , and the Hermite polynomials, . These relationships between the Gaussian and the Hermite polynomials are useful in linear scale-space analysis and applications to human and machine vision and image processing. The main objective of this paper is to extend these properties to a family of scaling functions that approximate the Gaussian function and to construct a family of Appell sequences of "scaling biorthogonal polynomials" that approximate the Hermite polynomials. 2000 Mathematics Subject Classification: 41A15, 41A30, 42C05, 42C15. Full text: PDF