Towards an Unbiased Comparison of CC, BCC, and FCC Lattices in Terms of Prealiasing

Viktor Vad, Balázs Csebfalvi, Peter Rautek, Meister 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

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.

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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 Csebfalvi and Peter Rautek and
               Meister 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",
  number =     "3",
  volume =     "33",
  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/",
}