Robert L. Cook
Abstract
Ray tracing, ray casting, and other forms of point sampling are important techniques in computer graphics, but their usefulness has been undermined by aliasing artifacts. In this paper it is shown that these artifacts are not an inherent part of point sampling, but a consequence of using regularly spaced samples. If the samples occur at appropriate nonuniformly spaced locations, frequencies above the Nyquist limit do not alias, but instead appear as noise of the correct average intensity. This noise is much less objectionable to our visual system than aliasing. In ray tracing, the rays can be stochastically distributed to perform a Monte Carlo evaluation of integrals in the rendering equation. This is called distributed ray tracing and can be used to simulate motion blur, depth of field, penumbrae, gloss, and translucency.
- 1 AMANATIDES, J. Ray tracing with cones. Comput. Graph. 18, 3 (July 1984), 129-145. Google Scholar
- 2 BALAKRISHNAN, A.V. On the problem of time jitter in sampling. IRE Trans. Inf. Theory {Apr. 1962), 226-236.Google Scholar
- 3 BLINN, J.F. Computer display of curved surfaces. Ph.D. dissertation, Computer Science Dept., Univ. of Utah, Salt Lake City, 1978. Google Scholar
- 4 BRACEWELL, R.N. The Fourier Transform and Its Applications. McGraw-Hill, New York, 1978.Google Scholar
- 5 COOK, R. L., PORTER, T., AND CARPENTER, L. Distributed ray tracing. Comput. Graph. 18, 3 {July 1984), 137-145. Google Scholar
- 6 CROW, F. The use of greyscale for improved raster display of vectors and characters. Comput. Graph. 12, 3 (Aug. 1978), 1-5. Google Scholar
- 7 DIPPE, M. A. Z., AND WOLD, E.H. Antialiasing through stochastic sampling. Comput. Graph. 19, 3 (July 1985), 69-78. Google Scholar
- 8 FEIBUSH, E., LEVOY, M., AND COOK, R.L. Synthetic texturing using digital filtering. Comput. Graph. 14, 3 (July 1980), 294-301. Google Scholar
- 9 GARDNER, G.Y. Simulation of natural scenes using textured quadric surfaces. Comput. Graph. 18, 3 (July 1984), 11-20. Google Scholar
- 10 GORAL, C. M., TORRANCE, K. E., GREENBERG, D. P., AND BATTAILE, B. Modeling the interaction of light between diffuse surfaces. Comput. Graph. 18, 3 (July 1984), 213-222. Google Scholar
- 11 HALTON, J.H. A retrospective and prospective survey of the Monte Carlo method. SIAM Rev. 12, 1 (Jan. 1970), 1-63.Google Scholar
- 12 KAJIVA, J.T. The rendering equation. Comput. Graph. 20, 4 (Aug. 1986), 143-150. Google Scholar
- 13 KAY, D. S., AND GREENBERG, D.P. Transparency for computer synthesized images. Comput. Graph. 13, 2 (Aug. 1979), 158-164. Google Scholar
- 14 LEE, M. E., REDNER, R. A., AND USELTON, S.P. Statistically optimized sampling for distributed ray tracing. Comput. Graph. 19, 3 (July 1985), 61-67. Google Scholar
- 15 NORTON, A., ROCKWOOD, A. P., AND SKOLMOSKI, P.T. Clamping: A method of antialiasing textured surfaces by bandwidth limiting in object space. Comput. Graph. 16, 3 (July 1982), 1-8. Google Scholar
- 16 PARAMOUNT PICTURES CORP. Young Sherlock Holmes. Stained glass man sequence by D. Carson, E. Christiansen, D. Conway, R. Cook, D. DiFrancesco, J. Ellis, L. Ellis, C. Good, J. Lasseter, S. Leffler, D. Muren, T. Noggle, E. Ostby, W. Reeves, D. Salesin, and K. Smith. Pixar and Lucasfilm Ltd., 1985.Google Scholar
- 17 PEARSON, D.E. Transmission and Display of Pictorial information. Pentech Press, London, 1975.Google Scholar
- 18 PIXAR. The Adventures of Andrd & Wally B. By L. Carpenter, E. Catmull, R. Cook, T. Duff, C. Good, J. Lasseter, S. Leffler, E. Ostby, T. Porter, W. Reeves, D. Salesin, and A. Smith. July 1984.Google Scholar
- 19 POTMESIL, M., AND CHAKRAVARTY, I. Modeling motion blur in computer-generated images. Comput. Graph. 17, 3 (July 1983), 389-399. Google Scholar
- 20 PRATT, W.K. Digital Image Processing. Wiley, New York, 1978. Google Scholar
- 21 ROTH, S. D. Ray casting for modeling solids. Comput. Graph. Image Process. 18 (1982), 109-144.Google Scholar
- 22 SHAPIRO, H. S., AND SILVERMAN, R.A. Alias-free sampling of random noise. SIAM J. 8, 2 {June 1960), 225-248.Google Scholar
- 23 SOCIETY OF PHOTOGRAPHIC SCIENTISTS AND ENGINEERS. SPSE Handbook of Photographic Science and Engineering. Wiley, New York, 1973.Google Scholar
- 24 WHITTED, T. An improved illumination model for shaded display. Commun. ACM 23, 6 (June 1980), 343-349. Google Scholar
- 25 WILLIAMS, D. R., AND COLLIER, R. Consequences of spatial sampling by a human photoreceptor mosaic. Science 221 (July 22, 1983), 385-387.Google Scholar
- 26 WILLIAMS, L. Pyramidal parametrics. Comput. Graph. 17, 3 (July 1983), 1-11. Google Scholar
- 27 YELLOTT, J. I., JR. Spectral consequences of photoreceptor sampling in the rhesus retina. Science 221 {July 22, 1983), 382-385.Google Scholar
Index Terms
- Stochastic sampling in computer graphics
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Reviews
William C. Lindow
This paper provides a very general summary of how stochastic sampling of an image reduces aliasing but adds noise to the resulting image. The reader is forced to accept the author's viewpoint because he provides no reasoning or rationale, with hard information, on why this form of sampling was developed or how. This makes it difficult for the reader to verify any of the author's statements and conclusions, follow up on the topic, or apply the sampling technique to actual images. A large bibliography is provided, which leaves it up to the reader to do the same research in order to arrive at the same conclusions. A quick review of discrete sampling of an image in computer graphics is presented, along with how uniform point sampling results in aliasing. Then, using the human eye as a basis, the author briefly discusses a Poisson disk distribution as a good random, nonuniform sampling distribution. The technique of jittering (adding noise to a sample location) is discussed in general terms, including how it can approximate a Poisson disk distribution. Jittering that is applied to distributed ray tracing is presented in general terms. The paper concludes with “examples” that are simply the results of stochastic sampling. The author provides little information about how this discrete sampling method is actually used to generate the pictures.
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