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Splatting Errors and Antialiasing
April-June 1998 (vol. 4 no. 2)
pp. 178-191

Abstract—This paper describes three new results for volume rendering algorithms utilizing splatting. First, an antialiasing extension to the basic splatting algorithm is introduced that mitigates the spatial aliasing for high-resolution volumes. Aliasing can be severe for high-resolution volumes or volumes where a high depth of field leads to converging samples along the perspective axis. Next, an analysis of the common approximation errors in the splatting process for perspective viewing is presented. In this context, we give different implementations, distinguished by efficiency and accuracy, for adding the splat contributions to the image plane. We then present new results in controlling the splatting errors and also show their behavior in the framework of our new antialiasing technique. Finally, current work in progress on extensions to splatting for temporal antialiasing is demonstrated. Here, we present a simple but highly effective scheme for adding motion blur to fast moving volumes.

[1] R.A. Crawfis and N. Max, "Texture Splats for 3D Scalar and Vector Field Visualization," Visualization 93, G.M. Nielson and D. Bergeron, eds., IEEE Computer Society Press, Los Alamitos, Calif., 1993, pp. 261-265.
[2] R. Crawfis, N. Max, and B. Becker, “Vector Field Visualization,” IEEE CG&A, Vol. 14, No. 5, Sept. 1994, pp. 50-56.
[3] R.A. Drebin, L. Carpenter, and P. Hanrahan, “Volume Rendering,” Computer Graphics (SIGGRAPH '88 Proc.), no. 22, pp. 65-74, 1988.
[4] P. Lacroute and M. Levoy, "Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation," Proc. Siggraph 94, ACM Press, New York, pp. 451-458.
[5] D. Laur and P. Hanrahan, Hierarchical Splatting: A Progressive Refinement Algorithm for Volume Rendering Proc. ACM SIGGRAPH, pp. 285-288, 1991.
[6] X. Mao, “Splatting of Non Rectilinear Volumes through Stochastic Resampling,” IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 2, pp. 156-170. June 1996.
[7] N. Max, "Optical Models for Direct Volume Rendering," IEEE Trans. Visualization and Computer Graphics, Vol. 1, No. 2, June 1995, pp. 99-108.
[8] K. Mueller and R. Yagel, “Fast Perspective Volume Rendering with Splatting by Utilizing a Ray-Driven Approach,” Proc. IEEE Visualization '96, pp. 65-72, Oct. 1996.
[9] K.L. Novins, F.X. Sillion, and D.P. Greenberg, "An Efficient Method for Volume Rendering Using Perspective Projection," Computer Graphics, vol. 24, no. 5, pp. 285-288, Nov. 1990.
[10] A.V. Oppenheim and R.W. Shafer, Digital Signal Processing.Englewood cliffs, N.J.: Prentice Hall, 1975.
[11] J.E. Swan et al., "An Anti-Aliasing Technique for Splatting," Proc. Visualization 97, IEEE Press, 1997, pp. 197-204.
[12] A. Van Gelder and K. Kim, “Direct Volume Rendering with Shading via Three-Dimensional Textures,” Proc. ACM/IEEE Symp. Volume Visualization, pp. 23-30, Oct. 1996.
[13] L. Westover, “Interactive Volume Rendering,” Proc. Chapel Hill Workshop Volume Visualization, C. Upson, ed., pp. 9-16, May 1989.
[14] L. Westover,“Footprint evaluation for volume rendering,” Proc. SIGGRAPH’90 (Dallas, Texas, Aug. 6-10, 1990). In Computer Graphics, vol. 24, no. 4, pp. 367-376, 1990.
[15] L.A. Westover, Splatting: A Parallel, Feed-Forward Volume Rendering Algorithm, doctoral thesis, Dept. of Computer Science, Univ. of North Carolina at Chapel Hill, Chapel Hill, N.C., 1991.
[16] R. Yagel, D.S. Ebert, J.N. Scott, and Y. Kurzion, “Grouping Volume Renderers for Enhanced Visualization in Computational Fluid Dynamics,” IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 2, pp. 117-132, June 1995.

Index Terms:
Volume rendering, splatting, direct volume rendering, resampling, reconstruction, antialiasing, perspective projection, motion blur.
Klaus Mueller, Torsten Möller, J. Edward Swan II, Roger Crawfis, Naeem Shareef, Roni Yagel, "Splatting Errors and Antialiasing," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 2, pp. 178-191, April-June 1998, doi:10.1109/2945.694987
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