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Hex-splines: a novel spline family for hexagonal lattices

Dimitri Van De Ville, Thierry Blu, Michael Unser, Wilfried Philips UGent, Ignace Lemahieu UGent and Rik Van de Walle UGent (2004) IEEE TRANSACTIONS ON IMAGE PROCESSING. 13(6). p.758-772
abstract
This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
bivariate splines, approximation theory, hexagonal lattices, sampling theory, FAST FOURIER-TRANSFORM, 2-DIMENSIONAL SIGNALS, B-SPLINES, RECONSTRUCTION, INTERPOLATION
journal title
IEEE TRANSACTIONS ON IMAGE PROCESSING
IEEE Trans. Image Process.
volume
13
issue
6
pages
758-772 pages
Web of Science type
Article
Web of Science id
000221466400003
JCR category
ENGINEERING, ELECTRICAL & ELECTRONIC
JCR impact factor
2.011 (2004)
JCR rank
27/209 (2004)
JCR quartile
1 (2004)
ISSN
1057-7149
DOI
10.1109/TIP.2004.827231
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
306153
handle
http://hdl.handle.net/1854/LU-306153
date created
2005-05-13 16:14:00
date last changed
2016-12-19 15:41:30
@article{306153,
  abstract     = {This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.},
  author       = {Van De Ville, Dimitri and Blu, Thierry and Unser, Michael and Philips, Wilfried and Lemahieu, Ignace and Van de Walle, Rik},
  issn         = {1057-7149},
  journal      = {IEEE TRANSACTIONS ON IMAGE PROCESSING},
  keyword      = {bivariate splines,approximation theory,hexagonal lattices,sampling theory,FAST FOURIER-TRANSFORM,2-DIMENSIONAL SIGNALS,B-SPLINES,RECONSTRUCTION,INTERPOLATION},
  language     = {eng},
  number       = {6},
  pages        = {758--772},
  title        = {Hex-splines: a novel spline family for hexagonal lattices},
  url          = {http://dx.doi.org/10.1109/TIP.2004.827231},
  volume       = {13},
  year         = {2004},
}

Chicago
Van De Ville, Dimitri, Thierry Blu, Michael Unser, Wilfried Philips, Ignace Lemahieu, and Rik Van de Walle. 2004. “Hex-splines: a Novel Spline Family for Hexagonal Lattices.” Ieee Transactions on Image Processing 13 (6): 758–772.
APA
Van De Ville, Dimitri, Blu, T., Unser, M., Philips, W., Lemahieu, I., & Van de Walle, R. (2004). Hex-splines: a novel spline family for hexagonal lattices. IEEE TRANSACTIONS ON IMAGE PROCESSING, 13(6), 758–772.
Vancouver
1.
Van De Ville D, Blu T, Unser M, Philips W, Lemahieu I, Van de Walle R. Hex-splines: a novel spline family for hexagonal lattices. IEEE TRANSACTIONS ON IMAGE PROCESSING. 2004;13(6):758–72.
MLA
Van De Ville, Dimitri, Thierry Blu, Michael Unser, et al. “Hex-splines: a Novel Spline Family for Hexagonal Lattices.” IEEE TRANSACTIONS ON IMAGE PROCESSING 13.6 (2004): 758–772. Print.