Research Area My research interests are in sampling and reconstruction issues in biomedical and scientific visualization applications. This area involves sampling theory, multivariate splines and multidimensional signal processing. Our workshop on Sampling and reconstruction: theory and applications, in Banff international research station (BIRS). Journal Publications Ye, W.; Portnoy, S.; Entezari, A.; Blackband, S.; Vemuri, B.; An Efficient Interlaced Multi-shell Sampling Scheme for Reconstruction of Diffusion Propagators, IEEE Transactions on Medical Imaging (TMI), vol.-, no.-, pp.-, accepted, 2011. Ye, W.; Entezari, A.; , A Geometric Construction of Multivariate Sinc Functions, IEEE Transactions on Image Processing (TIP), vol.-, no.-, pp.-, accepted, 2011. Mirzargar, M.; Entezari, A.; , Quasi Interpolation With Voronoi Splines, IEEE Transactions on Visualization and Computer Graphics (TVCG), vol.17, no.12, pp.1832-1841, Dec. 2011 (Presented at the IEEE Visualization conference). Meng, T.; Entezari, A.; Smith, B.; Möller, T.; Weiskopf, D.; Kirkpatrick, A. E.; , Visual Comparability of 3D Regular Sampling and Reconstruction, IEEE Transactions on Visualization and Computer Graphics (TVCG), vol.17, no.10, pp.1420-1432, Oct. 2011. Mirzargar, M.; Entezari, A.; , Voronoi Splines, IEEE Transactions on Signal Processing (TSP), vol.58, no.9, pp.4572-4582, Sept. 2010. Finkbeiner, B.; Entezari, A.; Van De Ville, D.; Möller, T.;, Efficient volume rendering on the body centered cubic lattice using box splines, Computers & Graphics (CAG), vol.34, no.4, pp.409-423, Aug. 2010. Entezari, A.; Mirzargar, M.; Kalantari, L.; , Quasi-interpolation on the Body Centered Cubic Lattice, Computer Graphics Forum (CGF), vol.28, no.3, pp.1015-1022, Jun. 2009. Alim, U.R.; Entezari, A.; Möller, T.; , The Lattice-Boltzmann Method on Optimal Sampling Lattices, IEEE Transactions on Visualization and Computer Graphics (TVCG) , vol.15, no.4, pp.630-641, July-Aug. 2009. Minho Kim; Entezari, A.; Peters, J.; , Box Spline Reconstruction On The Face-Centered Cubic Lattice, IEEE Transactions on Visualization and Computer Graphics (TVCG) , vol.14, no.6, pp.1523-1530, Nov.-Dec. 2008 (Presented at the IEEE Visualization conference). Entezari, A.; Van De Ville, D.; Möller, T.; , Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice, IEEE Transactions on Visualization and Computer Graphics (TVCG) , vol.14, no.2, pp.313-328, March-April 2008. Entezari, A.; Möller, T.; , Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice, IEEE Transactions on Visualization and Computer Graphics (TVCG) , vol.12, no.5, pp.1337-1344, Sept.-Oct. 2006 (Presented at the IEEE Visualization conference). Entezari, A.; Möller, T.; Vaisey, J.; , Subsampling matrices for wavelet decompositions on body centered cubic lattices, IEEE Signal Processing Letters (SPL) , vol.11, no.9, pp. 733- 735, Sept. 2004. Refereed Conference Publications Ye, W.; Portnoy, S.; Entezari, A.; Vemuri, B.C.; Blackband, S.J.; , Box spline based 3D tomographic reconstruction of diffusion propagators from MRI data, IEEE International Symposium on Biomedical Imaging (ISBI): From Nano to Macro, vol., no., pp.397-400, March 30 2011-April 2 2011. Entezari, A.; Unser, M.; , A box spline calculus for computed tomography, IEEE International Symposium on Biomedical Imaging (ISBI): From Nano to Macro, vol., no., pp.600-603, 14-17 April 2010. Wenxing Ye; Entezari, A.; Vemuri, B.C.; , Tomographic reconstruction of diffusion propagators from DW-MRI using optimal sampling lattices, IEEE International Symposium on Biomedical Imaging (ISBI): From Nano to Macro, vol., no., pp.788-791, 14-17 April 2010. Entezari, A., Uniform Sampling and Reconstruction of Trivariate Functions, Proceedings of the Eighth International Conference on Sampling Theory and Applications (SampTA), Marseille, France, May 2009. Meng, T.; Smith, B.; Entezari, A.; Kirkpatrick, A. E.; Weiskopf, D.; Kalantari, L.; and Möller, T.; On visual quality of optimal 3D sampling and reconstruction. Proceedings of Graphics Interface 2007 (GI '07). ACM, New York, NY, USA, 265-272. Entezari, A.; Meng, T.; Bergner, S.; Möller, T.; A Granular Three Dimensional Multiresolution Transform, EuroVis06 Joint Eurographics - IEEE VGTC Symposium on Visualization, 8-10 May, 2006, Lisbon, Portugal. pp. 267-274. Qiao, W.; Ebert, D.S.; Entezari, A.; Korkusinski, M.; Klimeck, G.; , VolQD: direct volume rendering of multi-million atom quantum dot simulations, IEEE Visualization, vol., no., pp. 319- 326, 23-28 Oct. 2005. Entezari, A.; Dyer, R.; Möller, T.; , Linear and cubic box splines for the body centered cubic lattice, IEEE Visualization, vol., no., pp. 11- 18, 10-15 Oct. 2004. Widjaya, H.; Möller, T.; Entezari, A.; , Voxelization in common sampling lattices, Proceedings of 11th Pacific Conference on Computer Graphics and Applications, vol., no., pp. 497- 501, 8-10 Oct. 2003. Entezari, A.; Scoggins, R.; Möller, T.; Machiraju, R.; , Shading for Fourier volume rendering, IEEE / ACM SIGGRAPH Symposium on Volume Visualization and Graphics, vol., no., pp. 131- 138, 28-29 Oct. 2002. Refereed Book Chapter Entezari, A.; Dyer, R.; Möller, T.; ,From Sphere Packing to the Theory of Optimal Lattice Sampling, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Springer Berlin Heidelberg, pp. 227-255, 2009 Dissertation Entezari, A., Optimal Sampling Lattices And Trivariate Box Splines, PhD Dissertation, 2007. Other Work Portnoy, S.; Ye, W.; Entezari, A.; Blackband, S.J.; Vemuri, B.C.; , A Novel Interlaced Sampling Scheme for Multi-Shell q-space Magnetic Resonance Microscopy, International Society for Magnetic Resonance in Medicine (ISMRM), 2011. Entezari, A., A note on the relationship between B-splines and the Riemann's Zeta Function on Integers. Entezari A., Morey J., Mueller K.,Ostromoukhov V., Van De Ville, D. ; Möller, T.; Point Lattices in Computer Graphics and Visualization Tutorial at IEEE Visualization 2005. Implementation and reproduction details Detailed experiments on the FCC lattice along with documentation and code are available. There you can also find code to incorporate into POV ray for rendering purposes. For experimenting with optimal lattices and a great list of implemented rendering algorithms, you may find vuVolume useful. This software is readily available on sourceforge.

Densest sphere packing by the Face Centered Cubic lattice. Body Centered Cubic lattice: the best sphere covering lattice.