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Multiresolution Analysis for Minimal Energy C r-Surfaces on Powell-Sabin Type Meshes

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5862))

Abstract

This paper is intended to provide a multiresolution analysis (MRA) scheme to obtain a sequence of C r-spline surfaces over a Powell-Sabin triangulation of a polygonal domain approximating a Lagrangian data set and minimizing a certain “energy functional”. We define certain non separable scaling and wavelet functions in bidimensional domains, and we give the decomposition and reconstruction formulas in the framework of lifting schemes. Two important applications of the theory are given: In the first one we develop an algorithm for noise reduction of signals. The second one is related to the localization of the regions where the energy of a given function is mostly concentrated. Some numerical and graphical examples for different test functions and resolution levels are given.

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Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Granada., Campus de Fuentenueva s/n, 18071, Granada, Spain

    Miguel A. Fortes, Pedro González & Miguel Pasadas

  2. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena (UPCT), Campus Muralla del Mar, 30202, Cartagena, Spain

    Maria Moncayo

Authors
  1. Miguel A. Fortes
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  2. Pedro González
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  3. Maria Moncayo
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  4. Miguel Pasadas
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Morten Dæhlen  & Tom Lyche  & 

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  3. INSA de Rennes, Rennes, France

    Jean-Louis Merrien

  4. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

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

    Larry L. Schumaker

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Fortes, M.A., González, P., Moncayo, M., Pasadas, M. (2010). Multiresolution Analysis for Minimal Energy C r-Surfaces on Powell-Sabin Type Meshes. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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