0507092 20240103222341.420190731235959.9 85069633891 000483631400021 10.1016/j.automatica.2019.108498 10 s. P cav_un_epca*02562180005-1098108Elsevier Optics Zernike polynomials Filter-generating systems Generating function Z-transform cav_un_auth*0347018 Honarvar Shakibaei Asli Barmak UTIA-B Zpracování obrazové informace Department of Image Processing ZOI ZOI Department of Image Processing MY Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101087 Flusser Jan UTIA-B Zpracování obrazové informace Department of Image Processing ZOI ZOI Department of Image Processing Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0293042 Zhao Y. GB cav_un_auth*0377796 Erkoyuncu J. A. GB http://library.utia.cas.cz/separaty/2019/ZOI/flusser-0507092.pdf https://www.sciencedirect.com/science/article/pii/S0005109819303590 cav_un_auth*0360230 GJ18-26018Y GA ČR cav_un_auth*0360229 GA18-07247S GA ČR This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. The case study shows a reliable way to evaluate Zernike polynomials with arbitrary degrees and azimuthal orders. WOS JD 20000 20200 20206 2020 4 4 A hod sml 4ah 4as 20231122144145.1 RVO:67985556 http://hdl.handle.net/11104/0298165 1 1 Department of Image Processing UTIA-B 10200 COMPUTER SCIENCE, THEORY & METHODS S Journal Publishing And Licensing Agreement 20190724 Publishing And Licensing Agreement 108498 3+4 Review Biochemistry Molecular Biology|Chemistry Multidisciplinary A AUTOMATION&CONTROLSYSTEMS|ENGINEERING.ELECTRICAL&ELECTRONIC 6.583 1.053 7.7 0.06703 2.35 39422 331 3.984 29.76 6.97 11438 Q1 5.150 506 Q1 96.66 87.5 Q1* Q1* 1.82 Q1 88.534 2019 Soubory v repozitáři: flusser-0507092.pdf, flusser-0507092-Publishing And Licensing Agreement.pdf 85069633891 SCOPUS PUBMED 000483631400021 WOS cav_un_epca*0256218 Automatica 0005-1098 1873-2836 Roč. 108 č. 1 2019 Elsevier