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Wavelet-Based Multiresolution with $$ \sqrt[n]{2} $$ Subdivision

In: Geometric Modelling

Author

Listed:
  • Lars Linsen

    (University of California, Center for Image Processing and Integrated Computing (CIPIC), Department of Computer Science)

  • Bernd Hamann

    (University of California, Center for Image Processing and Integrated Computing (CIPIC), Department of Computer Science)

  • Kenneth I. Joy

    (University of California, Center for Image Processing and Integrated Computing (CIPIC), Department of Computer Science)

  • Valerio Pascucci

    (Lawrence Livermore National Laboratory, Center for Applied Scientific Computing (CASC), Data Science Group)

  • Mark A. Duchaineau

    (Lawrence Livermore National Laboratory, Center for Applied Scientific Computing (CASC), Data Science Group)

Abstract

Multiresolution methods are a common technique used for dealing with large-scale data and representing it at multiple levels of detail. We present a multiresolution hierarchy construction based on $$ \sqrt[n]{2} $$ subdivision, which has all the advantages of a regular data organization scheme while reducing the drawback of coarse granularity. The $$ \sqrt[n]{2} $$ -subdivision scheme only doubles the number of vertices in each subdivision step regardless of dimension n. We describe the construction of 2D, 3D, and 4D hierarchies representing surfaces, volume data, and time-varying volume data, respectively. The 4D approach supports spatial and temporal scalability. For high-quality data approximation on each level of detail, we use downsampling filters based on n-variate B-spline wavelets. We present a B-spline wavelet lifting scheme for $$ \sqrt[n]{2} $$ -subdivision steps to obtain small or narrow filters. Narrow filters support adaptive refinement and out-of-core data exploration techniques.

Suggested Citation

  • Lars Linsen & Bernd Hamann & Kenneth I. Joy & Valerio Pascucci & Mark A. Duchaineau, 2004. "Wavelet-Based Multiresolution with $$ \sqrt[n]{2} $$ Subdivision," Springer Books, in: Stefanie Hahmann & Guido Brunnett & Gerald Farin & Ron Goldman (ed.), Geometric Modelling, pages 129-142, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0587-0_11
    DOI: 10.1007/978-3-7091-0587-0_11
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