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 i...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 cause</span><span style="font-size:10.0pt;font-family:"">s</span><span style="font-size:10.0pt;font-family:""> 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 <span>together by a global theoretical evaluation system called worst-case time co</span><span>mplexity. In this study, we have analyzed the selected algorithms and calculate</span>d 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 th</span><span style="font-size:10.0pt;font-family:"">ese</span><span style="font-size:10.0pt;font-family:""> criteria among the studied algorithms. According to time complexity, we have observed that although some algorithms </span><span style="font-size:10.0pt;font-family:"">such </span><span style="font-size:10.0pt;font-family:"">as Wee method and Modified Prata method were successful in having the smaller time complexit<span>ies, some other approaches did not make any significant difference compa</span>r</span><span style="font-size:10.0pt;font-family:"">ed</span><span style="font-size:10.0pt;font-family:""> to the classical algorithm.展开更多
文摘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 cause</span><span style="font-size:10.0pt;font-family:"">s</span><span style="font-size:10.0pt;font-family:""> 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 <span>together by a global theoretical evaluation system called worst-case time co</span><span>mplexity. In this study, we have analyzed the selected algorithms and calculate</span>d 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 th</span><span style="font-size:10.0pt;font-family:"">ese</span><span style="font-size:10.0pt;font-family:""> criteria among the studied algorithms. According to time complexity, we have observed that although some algorithms </span><span style="font-size:10.0pt;font-family:"">such </span><span style="font-size:10.0pt;font-family:"">as Wee method and Modified Prata method were successful in having the smaller time complexit<span>ies, some other approaches did not make any significant difference compa</span>r</span><span style="font-size:10.0pt;font-family:"">ed</span><span style="font-size:10.0pt;font-family:""> to the classical algorithm.
