Reconstruction of 3D objects from 2D cross-sections with the 4-point subdivision scheme adapted to sets

Computers and Graphics (Pergamon)

Volumn 35, Issue 3, 2011, Pages 741-746

  Kels, Shay ^a   Dyn, Nira ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

3D Reconstruction from cross sections; Interpolation of sets; The 4 point subdivision scheme

Indexed keywords

INTERPOLATION; ITERATIVE METHODS;

3D OBJECT; 3D RECONSTRUCTION; 4-POINT SUBDIVISION SCHEME; INTERPOLATORY SUBDIVISION; ITERATIVE REFINEMENT; PIECE-WISE; RESOLUTION METHODS; WEIGHTED AVERAGES;

IMAGE RECONSTRUCTION;

EID: 79957827652     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cag.2011.03.007     Document Type: Conference Paper

References (25)

1. aim@shape 〈 http://shapes.aim-at-shape.net 〉.
2. Aitkenhead AH. Polygon mesh voxelisation 〈 http://www.mathworks.com/ matlabcentral/fileexchange/27390-mesh-voxelisation 〉.
3. A. Albu, T. Beugeling, and D. Laurendeau A morphology-based approach for interslice interpolation of anatomical slices from volumetric images IEEE Transactions on Biomedical Engineering 55 8 2008
4. G. Barequet, M. Goodrich, A. Levi-Steiner, and D. Steiner Contour interpolation by straight skeletons Graphical Models 66 4 2004 245 260 (Pubitemid 38986159)
5. G. Barequet, and A. Vaxman Nonlinear interpolation between slices Proceedings of the 2007 ACM symposium on solid and physical modeling 2007 ACM 97 107 (Pubitemid 47582475)
6. A. Bors, L. Kechagias, and I. Pitas Binary morphological shape-based interpolation applied to 3-D tooth reconstruction IEEE Transactions on Medical Imaging 21 2 2002 100 108 (Pubitemid 34466424)
7. D. Cohen-Or, A. Solomovic, and D. Levin Three-dimensional distance field metamorphosis ACM Transactions on Graphics (TOG) 17 2 1998 116 141
8. Csébfalvi B, Neumann L, Kanitsar A, Gröller E. Smooth shape-based interpolation using the conjugate gradient method. In: Proceedings of vision, modeling, and visualization. Citeseer; 2002. p. 12330.
9. N. Dyn, and E. Farkhi Spline subdivision schemes for compact sets with metric averages Trends in Approximation Theory 2001 93 102
10. N. Dyn, and D. Levin Subdivision schemes in geometric modelling Acta Numerica 11 2003 73 144
11. N. Dyn, D. Levin, and J. Gregory A 4-point interpolatory subdivision scheme for curve design Computer Aided Geometric Design 4 4 1987 257 268 (Pubitemid 18595140)
12. G. Grevera, and J. Udupa Shape-based interpolation of multidimensional grey-level images IEEE Transactions on Medical Imaging 15 6 1996 881 892 (Pubitemid 126773989)
13. M. Iwanowski Morphological normalized binary object metamorphosis Computer Vision and Graphics 2006 626 632
14. Kels S, Dyn N. The 4-point subdivision scheme adapted to sets. Technical Report, Tel-Aviv University; 2010.
15. D. Levin Multidimensional reconstruction by set-valued approximations IMA Journal of Numerical Analysis 6 2 1986 173
16. Marker J, Braude I, Museth K, Breen D. Contour-based surface reconstruction using implicit curve fitting, and distance field filtering and interpolation. In: Proceedings of the international workshop on volume graphics. Citeseer; 2006. p. 95102.
17. C. Maurer Jr., R. Qi, and V. Raghavan A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions IEEE Transactions on Pattern Analysis and Machine Intelligence 1 2003 265 270
18. S. Raya, and J. Udupa Shape-based interpolation of multidimensional objects IEEE Transactions on Medical Imaging 9 1 1990 32 42 (Pubitemid 20712661)
19. F. Restle A metric and an ordering on sets Psychometrika 24 3 1959 207 220
20. G. Shephard, and R. Webster Metrics for sets of convex bodies Mathematika 12 1965 73 88
21. G. Turk, and J. O'Brien Shape transformation using variational implicit functions International conference on computer graphics and interactive techniques 1999 ACM New York, NY, USA
22. R. Veltkamp Shape matching: similarity measures and algorithms SMI 2001 IEEE Computer Society 188 197
23. D. Wang, O. Hassan, K. Morgan, and N. Weatherill Efficient surface reconstruction from contours based on two-dimensional Delaunay triangulation International Journal for Numerical Methods in Engineering 65 5 2006 734 751 (Pubitemid 43169440)
24. Whitaker R. Reducing aliasing artifacts in iso-surfaces of binary volumes 2000;vv:2332.
25. Yakersberg E. Morphing between geometric shapes using straight-skeleton-based interpolation. MSc thesis, Technio, Israel.