Filter-generating system of Zernike polynomials

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

2-D generating function of the zernike polynomials and their application for image classification

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. Since Zernike moments (ZMs) are invariant with respect to rotation, translation and scaling, the experimental schemes show the image classification applications by using the proposed algorithm

Zernike-moment-based image super resolution

Multiframe super-resolution (SR) reconstruction aims to produce a high-resolution (HR) image using a set of low-resolution (LR) images. In the process of reconstruction, fuzzy registration usually plays a critical role. It mainly focuses on the correlation between pixels of the candidate and the reference images to reconstruct each pixel by averaging all its neighboring pixels. Therefore, the fuzzy-registration-based SR performs well and has been widely applied in practice. However, if some objects appear or disappear among LR images or different angle rotations exist among them, the correlation between corresponding pixels becomes weak. Thus, it will be difficult to use LR images effectively in the process of SR reconstruction. Moreover, if the LR images are noised, the reconstruction quality will be affected seriously. To address or at least reduce these problems, this paper presents a novel SR method based on the Zernike moment, to make the most of possible details in each LR image for high-quality SR reconstruction. Experimental results show that the proposed method outperforms existing methods in terms of robustness and visual effects