EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Box Splines


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice

A. Entezari, D. Van De Ville, T. Möller

IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 313-328, March/April 2008.



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 C0 reconstruction. Then, the design is extended for higher degrees of continuity. We derive the explicit piecewise polynomial representations of the C0 and C2 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 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 the BCC lattice not only is generally a more accurate sampling pattern, but also allows for extremely efficient reconstructions that outperform tensor-product Cartesian reconstructions.


@ARTICLE(http://bigwww.epfl.ch/publications/entezari0801.html,
AUTHOR="Entezari, A. and Van De Ville, D. and M{\"{o}}ller, T.",
TITLE="Practical Box Splines for Reconstruction on the Body Centered
        Cubic Lattice",
JOURNAL="{IEEE} Transactions on Visualization and Computer Graphics",
YEAR="2008",
volume="14",
number="2",
pages="313--328",
month="March/April",
note="")

© 2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.