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Normal Multi-scale Transforms for Surfaces

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Curves and Surfaces (Curves and Surfaces 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

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Abstract

We prove well-posedness, convergence, and detail decay estimates for the normal triangular mesh multi-scale transform for C 1,α graph surfaces given in the simplest case when the subdivision rule S used for base point prediction is given by edge midpoint insertion. A restrictive assumption is that the initial triangular mesh needs to be quasi-regular and of small enough mesh-size. We also provide numerical evidence with other S for dyadic refinement (Butterfly, Loop), and propose a modification of the normal scheme resulting in improved detail decay for smooth surfaces.

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Author information

Authors and Affiliations

  1. School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany

    Peter Oswald

Authors
  1. Peter Oswald
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Editor information

Editors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. Laboratoire LJK, University Joseph Fourier, BP 53, 38420, Grenoble Cedex 9, France

    Patrick Chenin

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France

    Albert Cohen

  4. Laboratoire de Mathématiques, INSA Rouen, Avenue de l’Université, 76800, St. Etienne du Rouvray, France

    Christian Gout

  5. University of Oslo, DMA, Blindern, P.O.Box 1053, 0316, Oslo, Norway

    Tom Lyche

  6. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry Schumaker

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Oswald, P. (2012). Normal Multi-scale Transforms for Surfaces. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_34

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  • DOI: https://doi.org/10.1007/978-3-642-27413-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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