Abstract
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.
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Harizanov, S., Oswald, P. & Shingel, T. Normal Multi-scale Transforms for Curves. Found Comput Math 11, 617–656 (2011). https://doi.org/10.1007/s10208-011-9104-6
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DOI: https://doi.org/10.1007/s10208-011-9104-6
Keywords
- Nonlinear geometric multi-scale transforms
- Approximating subdivision schemes
- Lipschitz smoothness
- Curve representation
- Detail decay estimate