A Biorthogonal Wavelet Approach based on Dual Subdivision

In this paper a biorthogonal wavelet approach based on Doo‐Sabin subdivision is presented. In the dual subdivision like Doo‐Sabin scheme, all the old control vertices disappear after one subdivision step, which is a big challenge to the biorthogonal wavelet construction. In our approach, the barycen...

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Bibliographic Details
Published in:Computer graphics forum Vol. 27; no. 7; pp. 1815 - 1822
Main Authors: Zhang, Hui, Qin, Guiming, Qin, Kaihuai, Sun, Hanqiu
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.10.2008
Subjects:
and object representations
Hierarchy and geometric transformations
I.3.5 [Computational Geometry and Object Modeling]: Curve
I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations
solid
surface
Wavelet transforms
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:In this paper a biorthogonal wavelet approach based on Doo‐Sabin subdivision is presented. In the dual subdivision like Doo‐Sabin scheme, all the old control vertices disappear after one subdivision step, which is a big challenge to the biorthogonal wavelet construction. In our approach, the barycenters of the V‐faces corresponding to the old vertices are selected as the vertices associated with the scaling functions to construct the scaling space. The lifting scheme is used to guarantee the fitting quality of the wavelet transform, and a local orthogonalization is introduced with a discrete inner product operation to improve the computation efficiency. Sharp feature modeling based on extended Doo‐Sabin subdivision rules is also discussed in the framework of our wavelet construction. The presented wavelet construction is proven to be stable and effective by the experimental results.
Bibliography:ark:/67375/WNG-HT4873J3-2
istex:EDFFA4576151C0A8F941AD610A14BE3674F468CC
ArticleID:CGF1327
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2008.01327.x