This Article 
 Bibliographic References 
 Add to: 
Tricubic Interpolation of Discrete Surfaces for Binary Volumes
October-December 2003 (vol. 9 no. 4)
pp. 580-586

Abstract—Binary-defined 3D objects are common in volume graphics and medical imaging as a result of voxelization algorithms, segmentation methods, and binary operations such as clipping. Traditionally, renderings of binary objects suffer from severe image quality problems, especially when one tries to zoom-in and render the binary data from up close. We present a new rendering technique for discrete binary surfaces. The technique is based on distance-based normal estimation, an accelerated ray casting, and a tricubic interpolator. We demonstrate the quality achieved by our method and report on its interactive rendering speed.

[1] F. Allamandri, P. Cignoni, C. Montani, and R. Scopigno, Adaptively Adjusting Marching Cubes Output to Fit a Trilinear Reconstruction Filter Proc. Visualization in Scientific Computing '98 Workshop, pp. 25-34, 1998.
[2] J.G. Cleary and G. Wyvill, Analysis of an Algorithm for Fast Ray Tracing Using Uniform Space Subdivision The Visual Computer, vol. 4, no. 2, pp. 65-83, 1988.
[3] D. Cohen-Or, A. Kadosh, D. Levin, and R. Yagel, Smooth Boundary Surfaces from Binary 3D Data Sets Proc. Int'l Workshop Volume Graphics, Mar. 1999.
[4] D. Cohen-Or, E. Rich, U. Lerner, and V. Shenkar, A Real-Time Photo-Realistic Visual Flythrough IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 3, pp. 255-264, Sept. 1996.
[5] T. Fruhauf, Ray Casting Opaque Isosurfaces in Non-Regularly Gridded CFD Data Visualization in Scientific Computing, R. Scanteni, J. van Wijk, and P. Zanarini, eds., pp. 45-57, Wien: Springer, 1995.
[6] S.F.F. Gibson, Using Distance Maps for Accurate Surface Representation in Sampled Volumes Proc. IEEE 1998 Symp. Volume Visualization, pp. 23-30, 1998.
[7] B. Hamann, I. Trotts, and G. Farin, “On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 3, pp. 215-227, 1997.
[8] L. Hong, S. Muraki, A. Kaufman, D. Bartz, and T. He, "Virtual Voyage: Interactive Navigation In The Human Colon," Computer Graphics, pp. 27-34, Aug. 1997. ACM/SIGGRAPH Press.
[9] J. Huang, R. Crawfis, and D. Stredney, Edge Preservation in Volume Rendering Using Splatting Proc. 1998 Volume Visualization Symp., pp. 63-70, 1998.
[10] A. Kaufman, D. Cohen, and R. Yagel, "Volume Graphics," Computer, Vol. 26, No. 7, July 1993, pp. 51-64.
[11] Y. Livnat and C. Hansen, "View Dependent Isosurface Extraction", Proc. IEEE Visualization 98, ACM Press, 1998, pp. 175-180.
[12] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[13] S.R. Marschner and R.J. Lobb, "An Evaluation of Reconstruction Filters for Volume Rendering," Proc. Visualization '94, pp. 100-107, IEEE CS Press, Oct. 1994.
[14] K. Mueller, T. Möller,, and R. Crawfis,"Splatting without the Blur," Proc. Visualization 99, IEEE Press, 1999, pp. 363-370.
[15] T. Möller, R. Machiraju, K. Müller, and R. Yagel, “A Comparison of Normal Estimation Schemes,” Proc. IEEE Conf. Visualization 1997, pp. 19-26, Oct. 1997.
[16] S. Parker, P. Shirley, Y. Livnat, C. Hansen, and P. Sloan, Interactive Ray Tracing for Isosurface Rendering Proc. IEEE Visualization Conf., pp. 233-238, Oct. 1998.
[17] W.H. Press, Numerical Recipes in C. Cambridge Univ. Press, 1990.
[18] O. Shibolet and D. Cohen-Or, Coloring Voxel-Based Objects for Virtual Endoscopy Proc. 1998 IEEE Symp. Volume Visualization, pp. 15-22, 1998.
[19] U. Tiede, T. Schiemann, and K.H. Höhne, High Quality Rendering of Attributed Volume Data Proc. IEEE Visualization '98, pp. 255-262, 1998.
[20] R. Yagel, D. Cohen, and A. Kaufman, Normal Estimation in 3D Discrete Space The Visual Computer, vol. 8, nos. 5/6, pp. 278-291, June 1992.

Index Terms:
Volume visualization, volume rendering, ray casting, high order interpolation, distance function.
Arie Kadosh, Daniel Cohen-Or, Roni Yagel, "Tricubic Interpolation of Discrete Surfaces for Binary Volumes," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 4, pp. 580-586, Oct.-Dec. 2003, doi:10.1109/TVCG.2003.1260750
Usage of this product signifies your acceptance of the Terms of Use.