TITLE:
A Theoretical Comparison among Recursive Algorithms for Fast Computation of Zernike Moments Using the Concept of Time Complexity
AUTHORS:
Nasrin Bastani, Alireza Vard, Mehdi Jabalameli, Vahid Bastani
KEYWORDS:
Time Complexity, Uniform Model, Zernike Moments, Zernike Polynomi-als
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.4,
December
28,
2021
ABSTRACT: Zernike polynomials have been used in different
fields such as optics, astronomy, and digital image analysis for many years. To
form these polynomials, Zernike moments are essential to be determined. One of
the main issues in realizing the moments is using factorial terms in their
equation which causes higher time complexity. As
a solution, several methods have been presented to reduce the time complexity
of these polynomials in recent years. The purpose of this research is to study
several methods among the most popular recursive methods for fast Zernike
computation and compare them together by a
global theoretical evaluation system called worst-case time complexity. In this study, we have analyzed the
selected algorithms and calculated the worst-case time complexity for
each one. After that, the results are represented and explained and finally, a
conclusion has been made by comparing these criteria among the studied algorithms. According to time complexity, we
have observed that although some algorithms such as Wee method and Modified Prata method were successful in having the
smaller time complexities, some other
approaches did not make any significant difference compared to the classical algorithm.