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Splines Computation by Subdivision

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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

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Abstract

In this chapter, fast stable algorithms are presented, which compute splines’ values at dyadic and triadic rational points starting from their samples at integer grid points. The algorithms are implemented by the causal-anticausal recursive filtering of initial data samples, which is followed by iterated application of FIR filters. Extension of the algorithms to the multidimensional case is straightforward. A natural application of the presented subdivision algorithms is for upsampling of signals and images. A few upsampling examples are provided.

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References

  1. A. Averbuch, V. Zheludev, G. Fatakhov, E. Yakubov, Ternary interpolatory subdivision schemes originated from splines. Int. J. Wavelets Multiresolut. Inf. Process. 9(4), 611–633 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Dyn, Analysis of convergence and smoothness by the formalism of Laurent polynomials, in Tutorials on Multiresolution in Geometric Modelling, ed. by A. Iske, E. Quak, M.S. Floater (Springer, Berlin, 2002), pp. 51–68

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  3. N. Dyn, J.A. Gregory, D. Levin, Analysis of uniform binary subdivision schemes for curve design. Constr. Approx. 7(1), 127–147 (1991)

    Article  MathSciNet  Google Scholar 

  4. V. Zheludev, Local quasi-interpolatory splines and Fourier transforms. Sov. Math. Dokl. 31, 573–577 (1985)

    MATH  Google Scholar 

  5. V. Zheludev, Local spline approximation on a uniform mesh. U.S.S.R. Comput. Math. Math. Phys. 27(5), 8–19 (1987)

    Article  MATH  Google Scholar 

  6. V. Zheludev, Interpolatory subdivision schemes with infinite masks originated from splines. Adv. Comput. Math. 25(4), 475–506 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amir Z. Averbuch & Valery A. Zheludev

  2. Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

Authors
  1. Amir Z. Averbuch
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  2. Pekka Neittaanmäki
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  3. Valery A. Zheludev
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Correspondence to Amir Z. Averbuch .

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Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2016). Splines Computation by Subdivision . In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-22303-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-22303-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22302-5

  • Online ISBN: 978-3-319-22303-2

  • eBook Packages: EngineeringEngineering (R0)

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