# Reconstruction Gallery

‘Marschner-Lobb’ test function [1]
 ρ(x,y,z)= 1-sin(πz/2)+α(1+ρr((x2+y2)½)) 2(1+α)
where
• ρr(r)= cos(2πfMcos(πr/2))
• fM=6
• α=0.25
Level set 0.5 is rendered.
Reconstruction methods
 C¹ on FCC C² on BCC C¹ on Cartesian C² on Cartesian filter 6-dir. box spline 8-dir. box spline [2][3] tri-quadratic B-spline tri-cubic B-spline degree of filter 3 5 6 9 approx. order 3 4 3 4 stencil size 16 32 3³=27 4³=64
Reconstruction with various sampling density
 density C¹ on FCC C² on BCC C¹ on Cartesian C² on Cartesian (0.03)-3 (0.05)-3 (0.06)-3 (0.07)-3 (0.08)-3 (0.09)-3
Cut-away images
 density C¹ on FCC C² on BCC C¹ on Cartesian C² on Cartesian (0.05)-3 (0.06)-3 (0.07)-3 (0.08)-3 (0.09)-3
Cut-away Movie
 density C¹ on FCC C² on BCC (0.07)-3
Cut-away images of FCC and BCC
 density FCC|BCC FCC|BCC (0.05)-3 (0.06)-3 (0.07)-3 (0.08)-3 (0.09)-3
Cut-away images rotated by 45°
 density C¹ on FCC C² on BCC (0.05)-3 (0.06)-3 (0.07)-3 (0.08)-3 (0.09)-3
Top-view images
 density C¹ on FCC C² on BCC (0.05)-3 (0.06)-3 (0.07)-3 (0.08)-3 (0.09)-3
Carp dataset
 ↓ C¹ on Cartesian (256×256×512, density=1) lattice units = (0.78125,0.390625,1) ↓ C¹ on Cartesian (100×100×200, density=1/(256/100)³=0.0596) lattice units = ×(256/100) ↓ C¹ on FCC (63×63×126×4, density=4/(2*(256/126))³=0.0596) lattice units = ×(256/126) ↓ C¹ on Cartesian (cut in half, 100×100×200, density=1/(256/100)³=0.0596) lattice units = ×(256/100) ↓ C¹ on FCC (cut in half, 63×63×126×4, density=4/(2*(256/126))³=0.0596) lattice units = ×(256/126) ↓ C¹ on Cartesian (120×120×242, density=1/(256/120)³=0.1030) lattice units = ×(256/120) ↓ C¹ on FCC (75×75×150×4, density=4/(2*(256/150))³=0.1006) lattice units = ×(256/150)
 C¹ on Cartesian C¹ on FCC 120×120×242 75×75×150×4 0.1016 0.0998
Level set of the 6-direction box-spline
References
1. Stephen R. Marschner and Richard J. Lobb, “An Evaluation of Reconstruction Filters for Volume Rendering”, In Proceedings of Visualization '94, pages 100-107. Held in Washington, DC, October 1994.
2. Alireza Entezari and Ramsay Dyer and Torsten Möller, “Linear and Cubic Box Splines for the Body Centered Cubic Lattice”, pages 11-18, In Proceedings of the IEEE Conference on Visualization, October 2004.
3. Alireza Entezari, “Optimal Sampling Lattices and Trivariate Box Splines” (Ph.D thesis), Simon Fraser University, Vancouver, Canada, July 2007.
4. The Volume Library @University of Erlangen

last updated on 8 Sep. 2008 by Minho Kim (mhkim@cise.ufl.edu)