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A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

Author

Listed:
  • Abdellah Lamnii

    (Laboratoire MISI, Faculty of Science and Technology, Hassan First University of Settat, Settat 26000, Morocco)

  • Mohamed Yassir Nour

    (Laboratoire MISI, Faculty of Science and Technology, Hassan First University of Settat, Settat 26000, Morocco
    Laboratoire De Génie Informatique, de Production et de Maintenance, Université Lorraine, 10628 Metz, France)

  • Ahmed Zidna

    (Laboratoire De Génie Informatique, de Production et de Maintenance, Université Lorraine, 10628 Metz, France)

Abstract

In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

Suggested Citation

  • Abdellah Lamnii & Mohamed Yassir Nour & Ahmed Zidna, 2021. "A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2628-:d:659017
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    References listed on IDEAS

    as
    1. Siddiqi, Shahid S. & Salam, Wardat us & Rehan, Kashif, 2015. "A new non-stationary binary 6-point subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1227-1239.
    2. Siddiqi, Shahid S. & Salam, Wardat us & Rehan, Kashif, 2015. "Binary 3-point and 4-point non-stationary subdivision schemes using hyperbolic function," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 120-129.
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    Cited by:

    1. Dujuan Zhou & Zhanchuan Cai & Dan He, 2024. "A New Biorthogonal Spline Wavelet-Based K-Layer Network for Underwater Image Enhancement," Mathematics, MDPI, vol. 12(9), pages 1-16, April.

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