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Fast Ray-Tracing of Rectilinear Volume Data Using Distance Transforms
July-September 2000 (vol. 6 no. 3)
pp. 236-252

Abstract—This paper discusses and experimentally compares distance-based acceleration algorithms for ray-tracing of volumetric data with an emphasis on the Chessboard Distance (CD) voxel traversal. The acceleration of this class of algorithms is achieved by skipping empty macro regions, which are defined for each background voxel of the volume. Background voxels are labeled in a preprocessing phase by a value, defining the macro region size, which is equal to the voxel distance to the nearest foreground voxel. The CD algorithm exploits the chessboard distance and defines the ray as a nonuniform sequence of samples positioned at voxel faces. This feature assures that no foreground voxels are missed during the scene traversal. Further, due to parallelepipedal shape of the macro region, it supports accelerated visualization of cubic, regular, and rectilinear grids. The CD algorithm is suitable for all modifications of the ray tracing/ray casting techniques being used in volume visualization and volume graphics. However, when used for rendering based on local surface interpolation, it also enables fast search of intersections between rays and the interpolated surface, further improving speed of the process.

[1] J. Wallace,K. Elmquist,, and E. Haines,“A ray tracing algorithm for progressive radiosity,” Computer Graphics, vol. 23, no. 3, Siggraph’89 proc. pp. 315-324, 1989.
[2] L.M. Sobierajski and A.E. Kaufman, “Volumetric Ray Tracing,” Proc. 1994 Symp. Volume Visualization, IEEE Computer Society Press, Los Alamitos, Calif., 1994, pp. 11-18.
[3] A. Kaufman, D. Cohen, and R. Yagel, "Volume Graphics," Computer, Vol. 26, No. 7, July 1993, pp. 51-64.
[4] A. Kaufman, “Efficient Algorithms for 3-D Scan Conversion of Parametric Curves, Surfaces, and Volumes,” Computer Graphics, vol. 21, pp. 171-179, 1987.
[5] S. Wang and A. Kaufman, "Volume-Sampled 3D Modeling," IEEE Computer Graphics and Applications, Vol. 14, No. 5, 1994, pp. 26-32.
[6] M. Sramek and A.E. Kaufman, “Alias-Free Voxelization of Geometric Objects,” IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 3, pp. 251-267, July-Sept. 1999.
[7] A. Fujimoto, T. Takayu, and K. Iwata, "ARTS: Accelerated Ray-Tracing System," IEEE Computer Graphics and Applications, Vol. 6, No. 4, April 1986, pp. 16-26.
[8] J.C. 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, July 1988.
[9] J. Amanatides and A. Woo, “A Fast Voxel Traversal Algorithm for Ray Tracing,” Proc. EUROGRAPHICS '87, pp. 3-10, 1987.
[10] M. Levoy, “Efficient Ray Tracing of Volume Data,” ACM Trans. Graphics, vol. 9, no. 3, pp. 245-261, July 1990.
[11] K.J. Zuiderveld, A.H.J. Koning, and M.A. Viergever, “Acceleration of Ray-Casting Using 3D Distance Transforms,” Visualization in Biomedical Computing II, Proc. SPIE 1808, pp. 324-335, 1992.
[12] R. Yagel and Z. Shi, “Accelerating Volume Animation by Space-Leaping,” Proc. Visualization '93, pp. 62-84, 1993.
[13] D. Cohen and Z. Sheffer, “Proximity Clouds—An Acceleration Technique for 3D Grid Traversal,” The Visual Computer, vol. 11, pp. 27-38, 1994.
[14] M. Sramek, “Fast Surface Rendering from Raster Data by Voxel Traversal Using Chessboard Distance,” Proc. Visualization '94, pp. 188-195, Oct. 1994.
[15] G. Borgefors, “Distance Transforms in Digital Images,” Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
[16] M. Sramek, “Fast Ray-Tracing of Rectilinear Volume Data,” Proc. Virtual Environments and Scientific Visualization '96, pp. 201-210, 1996.
[17] 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.
[18] I. Bajla, I. Holländer, “Nonlinear Filtering of Magnetic Resonance Tomograms by Geometry-Driven Diffusion,” Machine Vision and Applications, no. 10, pp. 243-255, 1998.
[19] 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.
[20] M.J. Bentum, T. Malzbender, and B.B. Lichtenbelt, "Frequency Analysis of Gradient Estimators in Volume Rendering," IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 3, pp. 242-254, Sept. 1996.
[21] I. Carlbom, "Optimal Filter Design for Volume Reconstruction and Visualization," IEEE Visualization '93 Proc., pp. 54-61,San Jose, Calif., Oct. 1993.
[22] T. Möller, R. Machiraju, K. Mueller, and R. Yagel, “Evaluation and Design of Filters Using a Taylor Series Expansion,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 184-199, Apr.-June 1997.
[23] M. Sramek, Visualization of Volumetric Data by Ray Tracing. Austria: Austrian Computer Society, 1998.
[24] U. Tiede, T. Schiemann, and K.H. Höhne, “High Quality Rendering of Attributed Volume Data,” Proc. Visualization '98, pp. 255-262, 1998.
[25] R. Yagel, D. Cohen, and A. Kaufman, "Discrete Ray Tracing," IEEE Computer Graphics and Applications, Vol. 12, No. 5, Sept. 1992, pp. 19-28.
[26] J. Spackman and P. Willis, “The SMART Navigation of a Ray through an Oct-Tree,” Computers&Graphics, vol. 15, no. 2, pp. 185-194, 1991.
[27] O. Devillers, “The Macro-Regions: An Efficient Space Subdivision Structure for Ray Tracing,” Proc. Eurographics '89, pp. 27-38, 1989.
[28] R. Yagel and A. Kaufman, “Template-Based Volume Viewing,” Proc. Eurographics '92, pp. C153-C167, 1992.
[29] I. Holländer and M. Sramek, “An Interactive Tool for Manipulation and Presentation of 3D Tomographic Data,” Proc. CAR '93 Computer Assisted Radiology, pp. 278-383, 1993.

Index Terms:
Volume visualization, volume graphics, volume rendering, distance transforms, macro region, voxel traversal, speed up techniques, subvoxel precision.
Milos Sramek, Arie Kaufman, "Fast Ray-Tracing of Rectilinear Volume Data Using Distance Transforms," IEEE Transactions on Visualization and Computer Graphics, vol. 6, no. 3, pp. 236-252, July-Sept. 2000, doi:10.1109/2945.879785
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