Algorithm for computation of Zernike polynomials expansion coefficients

Abstract

A numerically efficient algorithm for expanding a function in a series of Zernike polynomials is presented. The algorithm evaluates the expansion coefficients through the standard 2-D integration formula derived from the Zernike polynomials' orthogonal properties. Quadratic approximations are used along with the function to be expanded to eliminate the computational problems associated with integrating the oscillatory behavior of the Zernike polynomials. This yields a procedure that is both fast and numerically accurate. Comparisons are made between the proposed scheme and a procedure using a nested 2-D Simpson's integration rule. The results show that typically at least a fourfold improvement in computational speed can be expected in practical use.

Region Of Interest Based Image Classification: A Study in MRI Brain Scan Categorization

“…This makes it impractical for many applications. This limitation has prompted considerable study of algorithms for the fast evaluation of Zernike moments [3,29,36]. Several algorithms have been proposed to speed up the computation.…”

“…Belkasim et al [3] introduced a fast algorithm based on the series expansion of radial polynomials. Parta et al [36] and Kintner [29] have proposed recurrence relations for fast computation of radial polynomials of Zernike moments. Chong et al [7] modified Kintners method so that it would be applicable for all cases.…”

Invariant Descriptors and Classifiers Combination for Recognition of Isolated Printed Tifinagh Characters

“…In this paper, the used approaches are: Hu moments [11], Legendre moments [12,13,14] and Zernike moments [15,16]. www.ijacsa.thesai.org…”

“…As these Zernike polynomials are orthogonal to each other, Zernike moments can represent the properties of an image with no redundancy or overlap of information between the moments [15]. Due to these characteristics, Zernike moments have been utilized as feature sets in many applications [16].…”

Application of Data Mining Tools for Recognition of Tifinagh Characters

“…The Tifinagh alphabet has several characters that can be obtained from others by a simple rotation, which makes invariant descriptors commonly used less effective. For this reason, we used a combination of Geodesic descriptors [5] and Zernike moments [6].…”