Biorthogonal Wavelets Based on Interpolatory Subdivision

Abstract

This article presents an efficient construction of biorthogonal wavelets built upon an interpolatory subdivision for quadrilateral meshes. The interpolatory subdivision scheme is first turned into a scheme for reversible primitive wavelet synthesis. Some desired properties are then incorporated in the primitive wavelet using the lifting scheme. The analysis and synthesis algorithms of the resulting new wavelet are finally obtained as local and in-place lifting operations. The wavelet inherits the advantage of refinement with added levels of resolution. Numerical experiments show that the lifted wavelet built upon interpolatory, subdivision has sufficient stability and better performance in dealing with closed or open semi-regular quadrilateral meshes compared with other existing wavelets for quadrilateral manifold meshes.