| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 335
J. Windmolders, E. Vanraes, P. Dierckx and A. Bultheel
Uniform Powell-Sabin spline wavelets
Abstract
This paper discusses how the subdivision scheme for uniform Powell-Sabin spline surfaces makes it possible to place those surfaces in a multiresolution context. We first show that the basis functions are translates and dilates of one vector of scaling functions. This defines a sequence of nested spaces. We then use the subdivision scheme as the prediction step in the lifting scheme and add an update step to construct wavelets that describe a sequence of complement spaces. Finally, as an example application, we use the new wavelet transform to reduce noise on a uniform Powell-Sabin spline surface.
report.pdf / mailto: J. Windmolders