Abstract
In this paper, we present an efficient biorthogonal wavelet construction for the ternary Loop subdivision based on the lifting scheme, and give the corresponding decomposition and reconstruction formulas. We apply the proposed algorithm to the progressive transmission and the denoising of 3D graphics, and show its sufficient stability and good performance by some numerical experiments. Since the usual input mesh does not possess the property of subdivision connectivity, while the multiresolution analysis based on subdivision surface requires the processed initial mesh to be semi-regular, we further propose a new rapid algorithm of constructing the initial mesh which not only possesses ternary subdivision connectivity but also approximates the given input mesh.
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