Browsing by Author "Flusser, Jan"

Now showing 1 - 4 of 4
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    2-D generating function of the zernike polynomials and their application for image classification
    (IEEE, 2019-12-19) Honarvar Shakibaei Asli, Barmak; Flusser, Jan; Zhao, Yifan
    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.
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    DCT/IDCT filter design for ultrasound image filtering
    (IEEE, 2021-05-05) Shakibaei, Barmak Honarvar; Flusser, Jan; Zhao, Yifan; Erkoyuncu, John Ahmet; Roy, Rajkumar
    In this paper, a new recursive structure based on the convolution model of discrete cosine transform (DCT) for designing of a finite impulse response (FIR) digital filter is proposed. In our derivation, we start with the convolution model of DCT-II to use its Z-transform for the proposed filter structure perspective. Moreover, using the same algorithm, a filter base implementation of the inverse DCT (IDCT) for image reconstruction is developed. The computational time experiments of the proposed DCT/IDCT filter(s) demonstrate that the proposed filters achieve faster elapsed CPU time compared to the others. The image filtering and reconstruction performance of the proposed approach on ultrasound images are presented to validate the theoretical framework.
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    Filter-generating system of Zernike polynomials
    (Elsevier, 2019-07-24) Honarvar Shakibaei Asli, Barmak; Flusser, Jan; Zhao, Yifan; Erkoyuncu, John Ahmet
    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.
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    ItemOpen Access
    Ultrasound image filtering and reconstruction using DCT/IDCT filter structure
    (IEEE, 2020-07-27) Honarvar Shakibaei Asli, Barmak; Flusser, Jan; Zhao, Yifan; Erkoyuncu, John Ahmet; Krishnan, Kajoli Banerjee; Farrokhi, Yasin; Roy, Rajkumar
    In this paper, a new recursive structure based on the convolution model of discrete cosine transform (DCT) for designing of a finite impulse response (FIR) digital filter is proposed. In our derivation, we start with the convolution model of DCT-II to use its Z-transform for the proposed filter structure perspective. Moreover, using the same algorithm, a filter base implementation of the inverse DCT (IDCT) for image reconstruction is developed. The computational time experiments of the proposed DCT/IDCT filter(s) demonstrate that the proposed filters achieve faster elapsed CPU time compared to the direct recursive structures and recursive algorithms for the DCT/IDCT with Arbitrary Length. Experimental results on clinical ultrasound images and comparisons with classical Wiener filter, non-local mean (NLM) filter and total variation (TV) algorithms are used to validate the improvements of the proposed approaches in both noise reduction and reconstruction performance for ultrasound images.