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Zernike polynomials

About: Zernike polynomials is a research topic. Over the lifetime, 4271 publications have been published within this topic receiving 68621 citations.


Papers
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Journal ArticleDOI
TL;DR: A new technique, denoted as q -recursive method, is proposed, specifically for fast computation of Zernike moments, which uses radial polynomials of fixed order p with a varying index q to compute ZERNike moments.

285 citations

Journal ArticleDOI
TL;DR: It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain.
Abstract: We give a detailed analysis of the accuracy of Zernike moments in terms of their discretization errors and the reconstruction power. It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle.

276 citations

Journal ArticleDOI
TL;DR: Correcting the temporal variation in the eye's wave aberration increases the Strehl ratio of the point spread function nearly 3 times, and increases the contrast of images of cone photoreceptors by 33% compared with images taken with only static correction of the eyes' higher order aberrations.
Abstract: We measured the improvement in retinal image quality provided by correcting the temporal variation in the eye's wave aberration with a closed-loop adaptive optics system This system samples the eye's wave aberration at rates up to 30 Hz Correction of the eye's aberrations can be completed in 025-05 seconds, resulting in residual rms wave-front errors as low as 01 microns for 68 mm pupils Real-time wave-front measurements were used to determine how effectively the spatial and temporal components of the eye's wave aberration were corrected The system provides dynamic correction of fluctuations in Zernike modes up to 5 th order with temporal frequency components up to 08 Hz Temporal performance is in good agreement with predictions based on theory Correction of the temporal variation in the eye's wave aberration increases the Strehl ratio of the point spread function nearly 3 times, and increases the contrast of images of cone photoreceptors by 33% compared with images taken with only static correction of the eye's higher order aberrations

275 citations

Journal ArticleDOI
TL;DR: In order to make the technique user-friendly a number of improvements have to be made, and are discussed in terms of the current level of technology and instrumentation.

273 citations

Journal ArticleDOI
TL;DR: Practical analysis of 3D Zernike invariants along with algorithms and computational details are provided along with a detailed discussion on influence of the algorithm parameters like the conversion into a volumetric function, number of utilized coefficients, etc.
Abstract: We advocate the usage of 3D Zernike invariants as descriptors for 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under rotation, translation and scaling. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of recently introduced spherical harmonics based descriptors. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance using several quality measures and based on experiments on the Princeton Shape Benchmark.

270 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023117
2022261
2021125
2020188
2019218
2018187