Journal of computational and applied mathematics vol:154 issue:1 pages:125-142
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. (C) 2003 Elsevier Science B.V. All rights reserved.