Title: Stable multiresolution analysis on triangles for surface compression
Authors: Maes, Jan ×
Bultheel, Adhemar #
Issue Date: 2006
Publisher: Kent State University
Series Title: Electronic Transactions on Numerical Analysis vol:25 pages:224-258
Abstract: Recently we developed multiscale spaces of C^1 piecewise quadratic polynomials on the Powell-Sabin 6-split of a triangulation relative to arbitrary polygonal domains Omega subset of R^2. These multiscale bases are weakly stable with respect to the L_2 norm. In this paper we prove that these multiscale spaces form a multiresolution analysis for the Banach space C^1(Omega) and we show that the multiscale basis forms a strongly stable Riesz basis for the Sobolev spaces H^s(Omega) with s is an element of (1, 5/2). In other words, the norm of a function f is an element of H^s(Omega) can be determined from the size of the coefficients in the multiscale representation of f. This property makes the multiscale basis suitable for surface compression. A simple algorithm for compression is proposed and we give an optimal a priori error bound that depends on the smoothness of the input surface and on the number of terms in the compressed approximant.
ISSN: 1068-9613
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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