A granular three dimensional multiresolution transform

Authors:
Alireza Entezari;Tai Meng;Steven Bergner;Torsten Möllery
Affiliations:
School of Computing Science, Simon Fraser University, Vancouver, Canada;School of Computing Science, Simon Fraser University, Vancouver, Canada;School of Computing Science, Simon Fraser University, Vancouver, Canada;School of Computing Science, Simon Fraser University, Vancouver, Canada
Venue:
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Year:
2006

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Abstract

We propose a three dimensional multi-resolution scheme to represent volumetric data in resolutions which are powers of two, resolving the rigidity of the commonly used separable Cartesian multi-resolution schemes in 3D that only allow for change of resolution by a power of eight. Through in-depth comparisons with the counterpart resampling solutions on the Cartesian lattice, we demonstrate the superiority of our subsampling scheme. We derive and document the Fourier domain analysis of this representation. Using such an analysis one can obtain ideal and discrete multidimensional filters for this multi-resolution scheme.