Uniform Powell--Sabin spline wavelets

Authors:
Joris Windmolders;Evelyne Vanraes;Paul Dierckx;Adhemar Bultheel
Affiliations:
Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan, 200 A, Heverlee B-3001, Belgium;Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan, 200 A, Heverlee B-3001, Belgium;Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan, 200 A, Heverlee B-3001, Belgium;Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan, 200 A, Heverlee B-3001, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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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.