Multiresolution Wavelet Based Model for Large Irregular Volume Data Sets

Abstract

In this paper we propose a wavelet based model for large irregular volume data sets by exploiting a multiresolution model based on semi-regular tetrahedral meshes. In order to generate the multiresolution representation we use a wavelet based approach that allows compression and progressive transmission. Beginning with a semi-regular tetrahedral mesh Г∞(T) and applying the wavelet transform, we obtain a representation that consists of a coarse base mesh Г0(T) and a sequence of detail coefficients obtained from the sucessive decomposition of the mesh at different levels of resolution. The base mesh is the one at the lowest resolution and it does not have the connectivity subdivision property. The wavelet decomposition is obtained by defining a wavelet basis over tetrahedra generated by a regular subdivision method applied to an initial tetrahedron T. The obtained basis is a Haar-like one and forms an unconditional basis for Lp(T,Σ,μ), 1<p<∞, being μ the Lebesgue measure and Σ the σ-algebra generated from the tetrahedron T by the chosen subdivision method.