A Biorthogonal Wavelet Approach based on Dual Subdivision

Abstract

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.