√3-Subdivision-based biorthogonal wavelets

A new efficient biorthogonal wavelet analysis based on the root 3 subdivision is proposed in the paper by using the lifting scheme. Since the root 3 subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the root 3 subdivision is more balanced than the existing wavelet analyses on triangular meshes and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with root 3 subdivision connectivity. The root 3-subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, and multiresolution editing and rendering of 3D geometric models.