More Orthogonal Polynomials as Moments
نویسندگان
چکیده
An overview is given for classical orthogonal polynomials as moments for other classical orthogonal polynomials. Some combinatorial explanations and open problems are discussed.
منابع مشابه
Orthogonal Fourier-Mellin moments for invariant pattern recognition
Received July 7, 1993; revised manuscript received November 22, 1993; accepted December 14, 1993 We propose orthogonal Fourier-Mellin moments, which are more suitable than Zernike moments, for scaleand rotation-invariant pattern recognition. The new orthogonal radial polynomials have more zeros than do the Zernike radial polynomials in the region of small radial distance. The orthogonal Fourier...
متن کاملImage representation using separable two-dimensional continuous and discrete orthogonal moments
This paper addresses bivariate orthogonal polynomials, which are a tensor product of two different orthogonal polynomials in one variable. These bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments. Some elementary properties of the proposed continuous Chebyshev–Gegenbauer moments (CGM), Gegenbauer–Legendre moments (GLM), and Chebys...
متن کاملImage Analysis by Discrete Orthogonal Hahn Moments
Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on thi...
متن کاملSome new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملA Comparative Study on Discrete Orthonormal Chebyshev Moments and Legendre Moments for Representation of Printed Characters
Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...
متن کامل