BLaC-wavelets: a multiresolution analysis with non-nested spaces

In the last five years, there has been numerous applications of wavelets and multiresolution analysis in many fields of computer graphics as different as geometric modelling, volume visualization or illumination modelling. Classical multiresolution analysis is based on the knowledge of a nested set of functional spaces in which the successive approximations of a given function converge to that function, and can be efficiently computed. This paper first proposes a theoretical framework which enables multiresolution analysis even if the functional spaces are not nested, as long as they still have the property that the successive approximations converge to the given function. Based on this concept, we finally introduce a new multiresolution analysis with exact reconstruction for large data sets defined on uniform grids. We construct a one-parameter family of multiresolution analyses which is a blending of Haar and linear multiresolution, using BLaC (Blending of Linear and Constant) wavelets.