关键词: 多分辨率分析, 细分小波, 细分小波紧框架, 渐进传输, 去噪

Abstract: Multiresolution analysis based on subdivision wavelets is an important method of 3D graphics processing.Many applications of this method including compression，denoising，progressive transmission，and multiresolution editing have been studied and developed.Recently Maria Charina et al have proposed a completely new theory of multiresolution analysis based on subdivision wavelet tight frames，which makes its practical applications to 3D graphics become a new subject worthy of investigation.Since the assumption of multiresolution analysis based on subdivision surface is that the input mesh is semi-regular，in the present paper a new rapid algorithm of constructing meshes which not only have subdivision connectivity but also approximate to the input mesh is proposed.Furthermore，based on the study of the new theory，the decomposition and reconstruction formulas of Loop subdivision wavelet tight frames are given in detail.Then the algorithm is implemented and applied to the progressive transmission and denoising of 3D graphics.In the last of the paper，by comparing it with the biorthogonal Loop subdivision wavelets of Bertram，the numerical results illustrate the good performance of the new technique.

Key words: multiresolution analysis, subdivision wavelets, subdivision wavelet tight frames, progressive transmission, denoising