Some applications of Loop-subdivision wavelet tight frames to the processing of 3D graphics

Abstract

Multiresolution analysis based on subdivision wavelets is an important method of 3D graphics processing. Many applications of this method have been studied and developed, including denoising, compression, progressive transmission, multiresolution editing and so on. Recently Charina and Stockler firstly gave the explicit construction of wavelet tight frame transform for subdivision surfaces with irregular vertices, which made its practical applications to 3D graphics became a subject worthy of investigation. Based on the works of Charina and Stockler, we present in detail the wavelet tight frame decomposition and reconstruction formulas for Loop-subdivision scheme. We further implement the algorithm and apply it to the denoising, compression and progressive transmission of 3D graphics. By comparing it with the biorthogonal Loop-subdivision wavelets of Bertram, the numerical results illustrate the good performance of the algorithm. Since multiresolution analysis based on subdivision wavelets or subdivision wavelet tight frames requires the input mesh to be semi-regular, we also propose a simple remeshing algorithm for constructing meshes which not only have subdivision connectivity but also approximate the input mesh.