Optimal Regular Volume Sampling

Thomas Theußl ¹      Torsten Möller ²      Meister Eduard Gröller ¹

1Institute of Computer Graphics and Algorithms Vienna University of Technology

2Graphics, Usability, and Visualization Lab Simon Fraser University

Figure 1: CT scans of a lobster and a tooth, represented on Cartesian and body-centered cubic grids (left and right images, respectively). The representation via body-centered cubic grids requires approximately 30% less samples.

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% fewer 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.

Key words: volume data, Cartesian grid, close packing, hexagonal sampling, body centered cubic

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