Viktor Vad, Balázs Csébfalvi, Peter Rautek, Eduard Gröller
Towards an Unbiased Comparison of CC, BCC, and FCC Lattices in Terms of Prealiasing
Computer Graphics Forum, 33(3):81-90, June 2014.
Information
- Publication Type: Journal Paper with Conference Talk
- Workgroup(s)/Project(s):
- Date: June 2014
- Journal: Computer Graphics Forum
- Volume: 33
- Number: 3
- Location: Swansea, Wales, UK
- Lecturer: Viktor Vad
- Event: Euro Vis 2014
- Conference date: 9. June 2014 – 13. June 2014
- Pages: 81 – 90
- Keywords: Image representation—Volumetric, Picture/Image Generation—Display algorit, Categories and Subject Descriptors
Abstract
In the literature on optimal regular volume sampling, the Body-Centered Cubic (BCC) lattice has been proven to be optimal for sampling spherically band-limited signals above the Nyquist limit. On the other hand, if the sampling frequency is below the Nyquist limit, the Face-Centered Cubic (FCC) lattice was demonstrated to be optimal in reducing the prealiasing effect. In this paper, we confirm that the FCC lattice is indeed optimal in this sense in a certain interval of the sampling frequency. By theoretically estimating the prealiasing error in a realistic range of the sampling frequency, we show that in other frequency intervals, the BCC lattice and even the traditional Cartesian Cubic (CC) lattice are expected to minimize the prealiasing. The BCC lattice is superior over the FCC lattice if the sampling frequency is not significantly below the Nyquist limit. Interestingly, if the original signal is drastically undersampled, the CC lattice is expected to provide the lowest prealiasing error. Additionally, we give a comprehensible clarification that the sampling efficiency of the FCC lattice is lower than that of the BCC lattice. Although this is a well-known fact, the exact percentage has been erroneously reported in the literature. Furthermore, for the sake of an unbiased comparison, we propose to rotate the Marschner-Lobb test signal such that an undue advantage is not given to either lattice.Additional Files and Images
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Weblinks
BibTeX
@article{Rautek_Peter_2014_TUC,
title = "Towards an Unbiased Comparison of CC, BCC, and FCC Lattices
in Terms of Prealiasing",
author = "Viktor Vad and Bal\'{a}zs Cs\'{e}bfalvi and Peter Rautek and
Eduard Gr\"{o}ller",
year = "2014",
abstract = "In the literature on optimal regular volume sampling, the
Body-Centered Cubic (BCC) lattice has been proven to be
optimal for sampling spherically band-limited signals above
the Nyquist limit. On the other hand, if the sampling
frequency is below the Nyquist limit, the Face-Centered
Cubic (FCC) lattice was demonstrated to be optimal in
reducing the prealiasing effect. In this paper, we confirm
that the FCC lattice is indeed optimal in this sense in a
certain interval of the sampling frequency. By theoretically
estimating the prealiasing error in a realistic range of the
sampling frequency, we show that in other frequency
intervals, the BCC lattice and even the traditional
Cartesian Cubic (CC) lattice are expected to minimize the
prealiasing. The BCC lattice is superior over the FCC
lattice if the sampling frequency is not significantly below
the Nyquist limit. Interestingly, if the original signal is
drastically undersampled, the CC lattice is expected to
provide the lowest prealiasing error. Additionally, we give
a comprehensible clarification that the sampling efficiency
of the FCC lattice is lower than that of the BCC lattice.
Although this is a well-known fact, the exact percentage has
been erroneously reported in the literature. Furthermore,
for the sake of an unbiased comparison, we propose to rotate
the Marschner-Lobb test signal such that an undue advantage
is not given to either lattice.",
month = jun,
journal = "Computer Graphics Forum",
volume = "33",
number = "3",
pages = "81--90",
keywords = " Image representation—Volumetric, Picture/Image
Generation—Display algorit, Categories and Subject
Descriptors",
URL = "https://www.cg.tuwien.ac.at/research/publications/2014/Rautek_Peter_2014_TUC/",
}