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Abstract

The classification of volumetric data sets as well as their rendering algorithms are typically based on the representation of the underlying grid. Grid structures based on a Cartesian lattice are the de-facto standard for regular representations of volumetric data. In this paper we introduce a more general concept of regular grids for the representation of volumetric data. We demonstrate that a specific type of regular lattice - the so-called body-centered cubic - is able to represent the same data set as a Cartesian grid to the same accuracy but with 29.3% less samples. This speeds up traditional volume rendering algorithms by the same ratio, which we demonstrate by adopting a splatting implementation for these new lattices. We investigate different filtering methods required for computing the normals on this lattice. The lattice representation results also in lossless compression ratios that are better than previously reported. Although other regular grid structures achieve the same sample efficiency, the body-centered cubic is particularly easy to use. The only assumption necessary is that the underlying volume is isotropic and band-limited - an assumption that is valid for most practical data sets.

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BibTeX

@techreport{Theussl-2001-ORS,
  title =      "Optimal Regular Volume Sampling",
  author =     "Thomas Theu{\ss}l and Torsten M\"{o}ller and Meister Eduard
               Gr\"{o}ller",
  year =       "2001",
  abstract =   "The classification of volumetric data sets as well as their
               rendering algorithms are typically based on the
               representation of the underlying grid. Grid structures based
               on a Cartesian lattice are the de-facto standard for regular
               representations of volumetric data. In this paper we
               introduce a more general concept of regular grids for the
               representation of volumetric data. We demonstrate that a
               specific type of regular lattice - the so-called
               body-centered cubic - is able to represent the same data set
               as a Cartesian grid to the same accuracy but with 29.3% less
               samples. This speeds up traditional volume rendering
               algorithms by the same ratio, which we demonstrate by
               adopting a splatting implementation for these new lattices.
               We investigate different filtering methods required for
               computing the normals on this lattice. The lattice
               representation results also in lossless compression ratios
               that are better than previously reported. Although other
               regular grid structures achieve the same sample efficiency,
               the body-centered cubic is particularly easy to use. The
               only assumption necessary is that the underlying volume is
               isotropic and band-limited - an assumption that is valid for
               most practical                  data sets.",
  month =      apr,
  number =     "TR-186-2-01-10",
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  keywords =   "body centered cubic, hexagonal sampling, close packing,
               Cartesian grid, volume data",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2001/Theussl-2001-ORS/",
}