Towards an unbiased comparison of CC, BCC, and FCC lattices in terms of prealiasing

Handle URI:
http://hdl.handle.net/10754/575715
Title:
Towards an unbiased comparison of CC, BCC, and FCC lattices in terms of prealiasing
Authors:
Vad, Viktor; Csébfalvi, Balázs; Rautek, Peter; Gröller, Eduard M.
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. © 2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Wiley-Blackwell
Journal:
Computer Graphics Forum
Issue Date:
Jun-2014
DOI:
10.1111/cgf.12364
Type:
Article
ISSN:
01677055
Sponsors:
This work was supported by the KAUST Visual Computing Center and OTKA K-101527.
Appears in Collections:
Articles; Visual Computing Center (VCC); Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorVad, Viktoren
dc.contributor.authorCsébfalvi, Balázsen
dc.contributor.authorRautek, Peteren
dc.contributor.authorGröller, Eduard M.en
dc.date.accessioned2015-08-24T08:36:26Zen
dc.date.available2015-08-24T08:36:26Zen
dc.date.issued2014-06en
dc.identifier.issn01677055en
dc.identifier.doi10.1111/cgf.12364en
dc.identifier.urihttp://hdl.handle.net/10754/575715en
dc.description.abstractIn 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. © 2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.en
dc.description.sponsorshipThis work was supported by the KAUST Visual Computing Center and OTKA K-101527.en
dc.publisherWiley-Blackwellen
dc.subjectCategories and Subject Descriptors (according to ACM CCS)en
dc.subjectI.3.3 [Computer Graphics]: Picture/Image Generation - Display algorithmsen
dc.subjectI.4.10 [Image Processing and Computer Vision]: Image representation - Volumetricen
dc.titleTowards an unbiased comparison of CC, BCC, and FCC lattices in terms of prealiasingen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalComputer Graphics Forumen
dc.contributor.institutionTampere University of Technology, Finlanden
dc.contributor.institutionBudapest University of Technology and Economics, Hungaryen
dc.contributor.institutionVienna University of Technology, Austriaen
dc.contributor.institutionVRVis Research Center, Austriaen
kaust.authorRautek, Peteren
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