Generalized B-spline subdivision-surface wavelets for geometry compression

We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogona...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2004-05, Vol.10 (3), p.326-338
Main Authors: Bertram, M., Duchaineau, M.A., Hamann, B., Joy, K.I.
Format: Article
Language:English
Subjects:
Algorithms
Arithmetic
Computer Graphics
Computer Society
Data Compression - methods
Discrete wavelet transforms
Geometry
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Imaging, Three-Dimensional - methods
Spline
Studies
Surface reconstruction
Surface waves
Topology
Wavelet coefficients
Wavelet transforms
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Summary:We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail is expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform is computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2004.1272731