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Application of CCC–Schoenberg operators on image resampling

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Abstract

Image resampling is a widely used tool in image processing. The upsampling increases the number of pixels and introduces new information to the image which can have undesired effects, like ringing artifacts and oscillations, aliasing “jagged” lines effect, or introduces too much numerical diffusion. Histopolation upsampling methods produce much sharper images but are more prone to aliasing and ringing effect and oscillations which appear as spurious signals near sharp transitions in color intensity. In this paper, we propose an efficient and fast quasi-histopolation algorithm based on the Canonical Complete Chebyshev–Schoenberg operator approximations, applied dimension by dimension. These approximations, because of their shape preserving properties, avoid oscillations. Presented methods have several tunable parameters that control tension and shape properties of the approximation which are used to reduce the aliasing effect while keeping the image visually sharp. Numerical tests on real and artificial images demonstrate the effectiveness and show the computational efficiency of the proposed algorithm.

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  1. Available online at http://www.cipr.rpi.edu/resource/stills/kodak.html.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Tina Bosner

  2. Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000, Rijeka, Croatia

    Bojan Crnković

  3. Department for Fluid Mechanics and Computational Engineering, Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000, Rijeka, Croatia

    Jerko Škifić

Authors
  1. Tina Bosner
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  2. Bojan Crnković
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  3. Jerko Škifić
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Correspondence to Bojan Crnković.

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Work of the first author has been fully supported by the University of Zagreb, under the project “Numerical algorithms”, year 2018. Work of the second author has been fully supported by the University of Rijeka under the project number uniri-prirod-18-9.

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Bosner, T., Crnković, B. & Škifić, J. Application of CCC–Schoenberg operators on image resampling. Bit Numer Math 60, 129–155 (2020). https://doi.org/10.1007/s10543-019-00770-7

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