Multiresolutions Numerically from Subdivisions
Date
2010-12-02T23:05:36Z
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Abstract
In previous work we introduced a construction to produce multiresolutions from given subdivisions.
A portion of that construction required solving bilinear equations using a symbolic algebra system.
Here we replace the bilinear equations with a pair of linear equation systems, resulting in a completely
numerical construction. Diagrammatic tools provide assistance in carrying this out. The construction
is shown for an example of univariate subdivision. The results for a bivariate subdivision are given to
illustrate the construction's ability to handle multivariate meshes, as well as special points, without
requiring any modi cation of approach. The construction usually results in analysis and reconstruction
lters that are nite, since it seeks each lter locally for the neighborhood of the mesh to which it
applies. The use of a set of lters constructed in this way is compared with lters based on spline
wavelets for image compression to show that the construction can yield satisfactory results.
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Keywords
Subdivision, refinement, multiresolution