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Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
March/April 2008 (vol. 14 no. 2)
pp. 313-328
ASCII Text
x 
 
Alireza Entezari, Dimitri Van De Ville, Torsten Möller, "Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 313-328, March/April, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2007.70429,
author = {Alireza Entezari and Dimitri Van De Ville and Torsten Möller},
title = {Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {14},
number = {2},
issn = {1077-2626},
year = {2008},
pages = {313-328},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2007.70429},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IS - 2
SN - 1077-2626
SP313
EP328
EPD - 313-328
A1 - Alireza Entezari,
A1 - Dimitri Van De Ville,
A1 - Torsten Möller,
PY - 2008
KW - Spline and piecewise polynomial approximation
KW - Spline and piecewise polynomial interpolation
KW - Splines
KW - Signal processing
KW - Reconstruction
KW - Finite volume methods
VL - 14
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
We introduce a family of box splines for efficient, accurate and smooth reconstruction of volumetric data sampled on the Body Centered Cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that allows for a linear $C^0$ reconstruction. Then, the design is extended for higher degrees of continuity. We derive the explicit piecewise polynomial representation of the $C^0$ and $C^2$ box splines that are useful for practical reconstruction applications. We further demonstrate that approximation in the shift-invariant space---generated by BCC-lattice shifts of these box splines---is \emph{twice} as efficient as using the tensor-product B-spline solutions on the Cartesian lattice (with comparable smoothness and approximation order, and with the same sampling density). Practical evidence is provided demonstrating that not only the BCC lattice is generally a more accurate sampling pattern, but also allows for extremely efficient reconstructions that outperform tensor-product Cartesian reconstructions.

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Index Terms:
Spline and piecewise polynomial approximation, Spline and piecewise polynomial interpolation, Splines, Signal processing, Reconstruction, Finite volume methods
Citation:
Alireza Entezari, Dimitri Van De Ville, Torsten Möller, "Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 313-328, March-April 2008, doi:10.1109/TVCG.2007.70429
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