Foundations of Computational Mathematics

, Volume 11, Issue 6, pp 617–656 | Cite as

Normal Multi-scale Transforms for Curves

  • S. Harizanov
  • P. OswaldEmail author
  • T. Shingel


Extending upon Daubechies et al. (Constr. Approx. 20:399–463, 2004) and Runborg (Multiscale Methods in Science and Engineering, pp. 205–224, 2005), we provide the theoretical analysis of normal multi-scale transforms for curves with general linear predictor S, and a more flexible choice of normal directions. The main parameters influencing the asymptotic properties (convergence, decay estimates for detail coefficients, smoothness of normal re-parametrization) of this transform are the smoothness of the curve, the smoothness of S, and its order of exact polynomial reproduction. Our results give another indication why approximating S may not be the first choice in compression applications of normal multi-scale transforms.


Nonlinear geometric multi-scale transforms Approximating subdivision schemes Lipschitz smoothness Curve representation Detail decay estimate 

Mathematics Subject Classification (2000)

65D17 65D15 65T60 26A16 


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Copyright information

© SFoCM 2011

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität KaiserslauternKaiserslauternGermany
  2. 2.School of Engineering and ScienceJacobs UniversityBremenGermany
  3. 3.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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