Document Detail

Practical box splines for reconstruction on the body centered cubic lattice.
MedLine Citation:
PMID:  18192712     Owner:  NLM     Status:  PubMed-not-MEDLINE    
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 {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.
Alireza Entezari; Dimitri Van De Ville; Torsten Möeller
Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  IEEE transactions on visualization and computer graphics     Volume:  14     ISSN:  1077-2626     ISO Abbreviation:  IEEE Trans Vis Comput Graph     Publication Date:    2008 Mar-Apr
Date Detail:
Created Date:  2008-01-14     Completed Date:  2008-04-02     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9891704     Medline TA:  IEEE Trans Vis Comput Graph     Country:  United States    
Other Details:
Languages:  eng     Pagination:  313-28     Citation Subset:  -    
School of Computer Science, Simon Fraser University, Burnaby, BC, Canada.
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