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Normal Multiresolution Approximation of Curves

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Abstract

A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular, we show that these properties critically depend on the underlying subdivision scheme and that, in general, the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA

    Ingrid Daubechies, Olof Runborg & Wim Sweldens

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  1. Ingrid Daubechies
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  2. Olof Runborg
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  3. Wim Sweldens
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Correspondence to Ingrid Daubechies.

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Daubechies, I., Runborg, O. & Sweldens, W. Normal Multiresolution Approximation of Curves. Constr Approx 20, 399–463 (2004). https://doi.org/10.1007/s00365-003-0543-4

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  • DOI: https://doi.org/10.1007/s00365-003-0543-4

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