Practical box splines for reconstruction on the body centered cubic lattice

IEEE Transactions on Visualization and Computer Graphics
Alireza EntezariTorsten Möeller

Abstract

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.

References

Oct 31, 2000·IEEE Transactions on Medical Imaging·P ThévenazM Unser
Jan 15, 2005·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Dimitri Van De VilleRik Van de Walle
Mar 3, 2006·IEEE Transactions on Visualization and Computer Graphics·Hamish CarrJack Snoeyink
May 12, 2007·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Laurent Condat, Dimitri Van De Ville

❮ Previous
Next ❯

Citations

Jul 8, 2015·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Masih NilchianMichael Unser
Feb 12, 2011·IEEE Transactions on Visualization and Computer Graphics·Zahid HossainTorsten Möller
Jun 8, 2013·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Xie XuAlireza Entezari
Jul 13, 2013·IEEE Transactions on Visualization and Computer Graphics·Balázs Csébfalvi
Nov 8, 2008·IEEE Transactions on Visualization and Computer Graphics·Minho KimJörg Peters
Nov 8, 2008·IEEE Transactions on Visualization and Computer Graphics·Christian LedergerberHanspeter Pfister
Oct 29, 2011·IEEE Transactions on Visualization and Computer Graphics·Mahsa Mirzargar, Alireza Entezari
Oct 27, 2010·IEEE Transactions on Visualization and Computer Graphics·Usman R AlimLaurent Condat
Nov 3, 2010·IEEE Transactions on Visualization and Computer Graphics·Tai MengArthur E Kirkpatrick
May 9, 2009·IEEE Transactions on Visualization and Computer Graphics·Usman R AlimTorsten Möller
Mar 13, 2010·IEEE Transactions on Visualization and Computer Graphics·Balázs Csébfalvi
May 23, 2012·IEEE Transactions on Visualization and Computer Graphics·Minho Kim
Mar 31, 2010·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Kunal Narayan ChaudhuryMichael Unser
Mar 22, 2012·IEEE Transactions on Medical Imaging·Xie XuAlireza Entezari
Jul 22, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Wenxing Ye, Alireza Entezari
Mar 29, 2012·IEEE Transactions on Medical Imaging·Alireza EntezariMichael Unser
Jan 6, 2016·IEEE Transactions on Visualization and Computer Graphics·Kaloian Petkov, Arie E Kaufman
Jul 11, 2013·PloS One·Lukas ChristenDonna T Geddes
Dec 14, 2016·IEEE Transactions on Visualization and Computer Graphics·Elham Sakhaee, Alireza Entezari

❮ Previous
Next ❯

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

IEEE Transactions on Visualization and Computer Graphics
Minho KimJörg Peters
IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Dimitri Van De VilleRik Van de Walle
IEEE Transactions on Visualization and Computer Graphics
Balázs Csébfalvi
IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Laurent Condat, Dimitri Van De Ville
© 2021 Meta ULC. All rights reserved