This Article
	Subscribers, please Login Purchase article: $19 PDF HTML IEEE Xplore Subscribers RSS feed
	Share
	Email this Article to a friend
	Bibliographic References
	ASCII Text BibTex RefWorks Procite/RefMan
	Add to:
	Digg Furl Spurl Blink Simpy Google Del.icio.us Y!MyWeb
	Search
	Similar Articles Articles by Minho Kim Articles by Alireza Entezari Articles by Jörg Peters

Box Spline Reconstruction On The Face-Centered Cubic Lattice

November/December 2008 (vol. 14 no. 6)

pp. 1523-1530

[1] C. L. Bajaj, R. L. Holt, and A. N. Netravali, Rational parametrizations of nonsingular real cubic surfaces. ACM Trans. Graph., 17 (1): 1–31, 1998.
[2] I. Carlbom, Optimal Filter Design for Volume Reconstruction and Visualization. In Proceedings of the IEEE Conference on Visualization, pages 54–61, Oct. 1993.
[3] H. Carr, T. Möller, and J. Snoeyink, Artifacts Caused by Simplicial Subdivision. IEEE Transactions on Visualization and Computer Graphics, 12 (2): 231–242, 2006.
[4] T. Cooklev, Regular perfect-reconstruction filter banks and wavelet bases. Ph.D. dissertation, Tokyo University of Technology, Tokyo, Japan, 1995.
[5] B. Csébfalvi, Prefiltered gaussian reconstruction for high-quality rendering of volumetric data sampled on a body-centered cubic grid. In IEEE Visualization, pages 311–318, 2005.
[6] C. de Boor, B-form basics. In Geometric modeling, pages 131–148. SIAM, Philadelphia, PA, 1987.
[7] C. de Boor, A practical guide to splines, volume 27 of Applied Mathematical Sciences. Springer-Verlag, New York, revised edition, 2001.
[8] C. de Boor, K. Höllig, and S. Riemenschneider, Box splines, volume 98 of Applied Mathematical Sciences. Springer-Verlag, New York, 1993.
[9] S. C. Dutta Roy and B. Kumar, Handbook of Statistics, volume 10, chapter Digital Differentiators, pages 159–205. Elsevier Science Publishers B. V., North Holland, 1993.
[10] A. Entezari, Optimal Sampling Lattices and Trivariate Box Splines. PhD thesis, Simon Fraser University, Vancouver, Canada, July 2007.
[11] A. Entezari, R. Dyer, and T. Möller, Linear and Cubic Box Splines for the Body Centered Cubic Lattice. In Proceedings of the IEEE Conference on Visualization, pages 11–18, Oct. 2004.
[12] A. Entezari, T. Meng, S. Bergner, and T. Möller, A Granular Three Dimensional Multiresolution Transform. In Proceedings of the Eurographics/IEEE-VGTC Symposium on Visualization, pages 267–274, May 2006.
[13] A. Entezari, D. Van De Ville, and T. Moller, Practical box splines for reconstruction on the body centered cubic lattice. Visualization and Computer Graphics, IEEE Transactions on, 14 (2): 313–328, March–April 2008.
[14] G. Farin, Curves and surfaces for computer-aided geometric design. Computer Science and Scientific Computing. Academic Press Inc., San Diego, CA, fourth edition, 1997.
[15] R. B. Fuller United States Patent Office # 2,986,241 OCTET TRUSS, 1961.
[16] R. G. Keys, Cubic Convolution Interpolation for Digital Image Processing. IEEE Tran. Acoustics, Speech, and Signal Processing, 29 (6): 1153–1160, Dec. 1981.
[17] J. Kovačević and M. Vetterli, FCO sampling of digital video using perfect reconstruction filter banks. IEEE Trans. Image Proc., 2 (1): 118–122, January 1993.
[18] H. R. Künsch, E. Agrell, and F. A. Hamprecht, Optimal lattices for sampling. IEEE Transactions on Information Theory, 51 (2): 634–647, Feb. 2005.
[19] L. Linsen, V. Pascucci, M. A. Duchaineau, B. Hamann, and K. I. Joy, Hierarchical representation of time-varying volume data with "4th-root-of-2" subdivision and quadrilinear b-spline wavelets. In PG '02: Proceedings of the 10th Pacific Conference on Computer Graphics and Applications, page 346, Washington, DC, USA, 2002. IEEE Computer Society.
[20] S. R. Marschner and R. J. Lobb, An Evaluation of Reconstruction Filters for Volume Rendering. In Proceedings of the IEEE Conference on Visualization, pages 100–107, 1994.
[21] J. H. McClellan, The design of two-dimensional digital filters by transformations. In Proc. 7th Annu. Princeton Conf. Information Sciences and Systems, pages 247–251, Princeton, NJ, 1973.
[22] F. Meyer, Mathematical morphology: from two dimensions to three dimension s. Journal of Microscopy, 165 (1): 5–28, 1992.
[23] D. P. Mitchell and A. N. Netravali, Reconstruction Filters in Computer Graphics. In Computer Graphics (Proceedings of SIGGRAPH 88), volume 22, pages 221–228, Aug. 1988.
[24] T. Möller, K. Mueller, Y. Kurzion, R. Machiraju, and R. Yagel, Design of Accurate and Smooth Filters for Function and Derivative Reconstruction. Proceedings of the Symposium on Volume Visualization, pages 143–151, Oct 1998.
[25] A. Oppenheim and R. Schafer, Discrete-Time Signal Processing. Prentice Hall Inc., Englewoods Cliffs, NJ, 1989.
[26] D. P. Petersen and D. Middleton, Sampling and Reconstruction of WaveNumber-Limited Functions in N-Dimensional Euclidean Spaces. Information and Control, 5 (4): 279–323, Dec. 1962.
[27] W. Qiao, D. Ebert, A. Entezari, M. Korkusinski, and G. Klimeck, VolQD: Direct Volume Rendering of Multi-million Atom Quantum Dot Simulations. In Proceedings of the IEEE Conference on Visualization, pages 319–326, Oct. 2005.
[28] F. Qiu, F. Xu, Z. Fan, N. Neophytos, A. K. fman, and K. Mueller, Lattice-based volumetric global illumination. IEEE Transactions on Visualization and Computer Graphics, 13 (6): 1576–1583, 2007.
[29] T. Theußl, O. Mattausch, T. Möller, and E. Gröller, Reconstruction schemes for high quality raycasting of the body-centered cubic grid. TR-186-2-02-11, Institute of Computer Graphics and Algorithms, Vienna University of Technology, December 2002.
[30] T. Theußl, T. Möller, and E. Gröller, Optimal Regular Volume Sampling. In Proceedings of the IEEE Conference on Visualization 2001, pages 91–98, Oct 2001.
[31] P. Thévenaz, T. Blu, and M. Unser, Interpolation revisited. IEEE Transactions on Medical Imaging, 19 (7): 739–758, July 2000.
[32] D. Van De Ville,T. Blu, and M. Unser, On the Multidimensional Extension of the Quincunx Subsampling Matrix. IEEE Signal Processing Letters, 12 (2): 112–115, February 2005.