文章基本信息

标题：A Theoretical Comparison among Recursive Algorithms for Fast Computation of Zernike Moments Using the Concept of Time Complexity
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作者：Nasrin Bastani ; Alireza Vard ; Mehdi Jabalameli 等
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2021
卷号：11
期号：4
页码：304-326
DOI：10.4236/ajcm.2021.114020
语种：English
出版社：Scientific Research Publishing
摘要：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.
关键词：Time Complexity;Uniform Model;Zernike Moments;Zernike Polynomi-als