Efficient wavelet construction with Catmull-Clark subdivision

This paper presents an efficient biorthogonal wavelet construction with the generalized Catmull-Clark subdivision based on the lifting scheme. The subdivision wavelet construction scheme is applicable to all variants of Catmull-Clark subdivision, so it is more universal than the previous wavelet construction for the generalized bicubic B-spline subdivision. Because the analysis and synthesis algorithms of the wavelets are composed of a series of local and in-place lifting operations, they can be performed in linear time. The experiments have demonstrated the stability of the proposed wavelet analysis based on the ordinary Catmull-Clark subdivision. Moreover, the resulting Catmull-Clark subdivision wavelets have better fitting quality than the generalized bicubic B-spline subdivision wavelets at a similar computation cost.