Nonlinear Subdivision Schemes: Applications to Image Processing

  • Albert Cohen
  • Basarab Matei
Part of the Mathematics and Visualization book series (MATHVISUAL)


In classical subdivision schemes, some initial discrete data set v 0 is refined iteratively, following a prescribed linear rule which is summarized by
$$ {v^j} = S{v^{j - 1}} = \cdots = {S^j}{v^0} $$
where v j are the numerical data at resolution 2-j and S the subdivision operator. One is usually interested in the convergence properties of this process to some limit function f = S v 0. In the simplest setting the data v j belongs to the uniform grid 2-j ℤ and convergence means that sup k
$$ \left| {f({2^{ - j}}k) - v_k^j} \right| $$
goes to zero as j tends to +. The analysis of convergence can be performed by various methods, including Fourier analysis by Laurent polynomials [4], when the scheme is uniform.


Subdivision Scheme Multiresolution Analysis Laurent Polynomial Subdivision Algorithm Multiscale Representation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Albert Cohen
    • 1
  • Basarab Matei
    • 1
  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParisFrance

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