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Generalized B-spline subdivision-surface wavelets for geometry compression.

Martin Bertram1, Mark A Duchaineau, Bernd Hamann

  • 1FB Informatik, University of Kaiserslautern, Kauserslautern, Germany. bertram@informatik.uni-kl.de

IEEE Transactions on Visualization and Computer Graphics
|June 27, 2008
PubMed
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We developed a new wavelet transform for representing complex 3D shapes. This method efficiently compresses geometric data on surfaces with any topology using a lifting scheme and B-spline wavelets.

Area of Science:

  • Computer Graphics
  • Geometric Modeling
  • Wavelet Theory

Background:

  • Representing complex 3D geometries efficiently is crucial for various applications.
  • Existing methods often struggle with surfaces of arbitrary topology.
  • Multiresolution analysis and compression techniques are needed for large datasets.

Purpose of the Study:

  • To introduce a novel construction of lifted biorthogonal wavelets for surfaces.
  • To enable efficient compression and multiresolution representation of arbitrary topological surfaces.
  • To combine subdivision surfaces, B-spline wavelets, and the lifting scheme.

Main Methods:

  • Utilized local lifting operations on polygonal meshes with subdivision hierarchy.
  • Constructed wavelet transforms for bilinear, bicubic, and biquintic B-Spline subdivisions.

Related Experiment Videos

  • Employed integer arithmetic for lossless compression of control point coordinates.

    • Main Results:

    • Demonstrated a new wavelet transform applicable to surfaces of arbitrary two-manifold topology.
    • Achieved efficient and progressive representation of complex geometries.
    • Identified instability in the biquintic B-Spline construction while bilinear and bicubic performed well.

    Conclusions:

    • The proposed lifted biorthogonal wavelet transform offers a powerful tool for geometric data compression and multiresolution analysis.
    • The method is highly efficient and suitable for progressive transmission of complex geometries.
    • Further research may be needed to address the instability of higher-order B-Spline constructions.