Skip to main content
SpringerLink
Log in

Myths of Computer Graphics

  • Conference paper
Monte Carlo and Quasi-Monte Carlo Methods 2004

Summary

Computer graphics textbooks teach that sampling by deterministic patterns or even lattices causes aliasing, which only can be avoided by random, i.e. independent sampling. They recommend random samples with blue noise characteristic, which however are highly correlated due to their maximized minimum mutual distance. On the other hand the rendering software mental ray, which is used to generate the majority of visual effects in movies, entirely is based on parametric integration by quasi-Monte Carlo methods and consequently is strictly deterministic. For its superior quality the software even received a Technical Achievement Award (Oscar) by the American Academy of Motion Picture Arts and Sciences in 2003. Along the milestones of more than ten years of development of quasi-Monte Carlo methods in computer graphics, we point out that the two previous statements are not contradictory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BBD+00]_C. Betrisey, J. Blinn, B. Dresevic, B. Hill, G. Hitchcock, B. Keely, D. Mitchell, J. Platt, and T. Whitted, Displaced Filtering for Patterned Displays, Proc. Society for Information Display Symposium (2000), 296–299.

    Google Scholar 

  2. R. Cook, L. Carpenter, and E. Catmull, The REYES Image Rendering Architecture, Computer Graphics (SIGGRAPH’ 87 Proceedings), July 1987, pp. 95–102.

    Google Scholar 

  3. R. Cranley and T. Patterson, Randomization of number theoretic methods for multiple integration, SIAM Journal on Numerical Analysis 13 (1976), 904–914.

    Article  MathSciNet  Google Scholar 

  4. R. Cook, T. Porter, and L. Carpenter, Distributed Ray Tracing, Computer Graphics (SIGGRAPH’ 84 Conference Proceedings), 1984, pp. 137–145.

    Google Scholar 

  5. K. Dimitriev, S. Brabec, K. Myszkowski, and H.-P. Seidel, Interactive Global Illumination using Selective Photon Tracing, Rendering Techniques 2002 (Proc. 13th Eurographics Workshop on Rendering) (P. Debevec and S. Gibson, eds.), Springer, 2002, pp. 25–36.

    Google Scholar 

  6. H. Faure, Good Permutations for Extreme Discrepancy, J. Number Theory 42 (1992), 47–56.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Frolov and N. Chentsov, On the calculation of certain integrals dependent on a parameter by the Monte Carlo method, Zh. Vychisl. Mat. Fiz. 2 (1962), no. 4, 714–717, (in Russian).

    Google Scholar 

  8. I. Friedel and A. Keller, Fast Generation of Randomized Low-Discrepancy Point Sets, Monte Carlo and Quasi-Monte Carlo Methods 2000 (H. Niederreiter, K. Fang, and F. Hickernell, eds.), Springer, 2002, pp. 257–273.

    Google Scholar 

  9. A. Glassner, Principles of Digital Image Synthesis, Morgan Kaufmann, 1995.

    Google Scholar 

  10. P. Haeberli and K. Akeley, The Accumulation Buffer: Hardware Support for High-Quality Rendering, Computer Graphics (SIGGRAPH 90 Conference Proceedings), 1990, pp. 309–318.

    Google Scholar 

  11. S. Heinrich and A. Keller, Quasi-Monte Carlo Methods in Computer Graphics, Part I: The QMC-Buffer, Interner Bericht 242/94, University of Kaiserslautern, 1994.

    Google Scholar 

  12. _____ Quasi-Monte Carlo Methods in Computer Graphics, Part II: The Radiance Equation, Interner Bericht 243/94, University of Kaiserslautern, 1994.

    Google Scholar 

  13. E. Hlawka, Discrepancy and Riemann Integration, Studies in Pure Mathematics (L. Mirsky, ed.), Academic Press, New York, 1971, pp. 121–129.

    Google Scholar 

  14. J. Halton and G. Weller, Algorithm 247: Radical-inverse quasi-random point sequence, Comm. ACM 7 (1964), no. 12, 701–702.

    Article  Google Scholar 

  15. H. Jensen, Realistic Image Synthesis Using Photon Mapping, AK Peters, 2001.

    Google Scholar 

  16. A. Keller, A Quasi-Monte Carlo Algorithm for the Global Illumination Problem in the Radiosity Setting, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, eds.), Lecture Notes in Statistics, vol. 106, Springer, 1995, pp. 239–251.

    Google Scholar 

  17. _____, Quasi-Monte Carlo Methods in Computer Graphics: The Global Illumination Problem, Lectures in App. Math. 32 (1996), 455–469.

    MATH  Google Scholar 

  18. A. Keller, Quasi-Monte Carlo Radiosity, Rendering Techniques’ 96 (Proc. 7th Eurographics Workshop on Rendering) (X. Pueyo and P. Schröder, eds.), Springer, 1996, pp. 101–110.

    Google Scholar 

  19. _____, Instant Radiosity, SIGGRAPH 97 Conference Proceedings, Annual Conference Series, 1997, pp. 49–56.

    Google Scholar 

  20. _____, Quasi-Monte Carlo Methods for Photorealistic Image Synthesis, Ph.D. thesis, Shaker Verlag Aachen, 1998.

    Google Scholar 

  21. _____, The Quasi-Random Walk, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing 1996 (H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof, eds.), vol. 127, Springer, 1998, pp. 277–291.

    Google Scholar 

  22. _____, Hierarchical Monte Carlo Image Synthesis, Mathematics and Computers in Simulation 55 (2001), no. 1–3, 79–92.

    Google Scholar 

  23. _____, Trajectory Splitting by Restricted Replication, Interner Bericht 316/01, Universität Kaiserslautern, 2001.

    Google Scholar 

  24. _____, Strictly Deterministic Sampling Methods in Computer Graphics, SIGGRAPH 2003 Course Notes, Course #44: Monte Carlo Ray Tracing (2003).

    Google Scholar 

  25. _____, Stratification by Rank-1 Lattices, Monte Carlo and Quasi-Monte Carlo Methods 2002 (H. Niederreiter, ed.), Springer, 2004, pp. 299–313.

    Google Scholar 

  26. A. Keller and W. Heidrich, Interleaved Sampling, Rendering Techniques 2001 (Proc. 12th Eurographics Workshop on Rendering) (K. Myszkowski and S. Gortler, eds.), Springer, 2001, pp. 269–276.

    Google Scholar 

  27. J. Kajiya and T. Kay, Rendering Fur with Three Dimensional Textures, Computer Graphics (Proceedings of SIGGRAPH 89) 23 (1989), no. 3, 271–280.

    Article  Google Scholar 

  28. T. Kollig and A. Keller, Efficient Bidirectional Path Tracing by Randomized Quasi-Monte Carlo Integration, Monte Carlo and Quasi-Monte Carlo Methods 2000 (H. Niederreiter, K. Fang, and F. Hickernell, eds.), Springer, 2002, pp. 290–305.

    Google Scholar 

  29. _____, Efficient Multidimensional Sampling, Computer Graphics Forum 21 (2002), no. 3, 557–563.

    Article  Google Scholar 

  30. _____, Efficient Illumination by High Dynamic Range Images, Rendering Techniques 2003 (Proc. 14th Eurographics Symposium on Rendering) (P. Christensen and D. Cohen-Or, eds.), Springer, 2003, pp. 45–51.

    Google Scholar 

  31. C. Lemieux, L’utilisation de règles de réseau en simulation comme technique de réduction de la variance, Ph.d. thesis, Université de Montréal, département d’informatique et de recherche opérationnelle, May 2000.

    Google Scholar 

  32. G. Larcher and F. Pillichshammer, Walsh Series Analysis of the L2-Discrepancy of Symmetrisized Point Sets, Monatsh. Math. 132 (2001), 1–18.

    Article  MathSciNet  Google Scholar 

  33. J. Matoušek, On the L2-discrepancy for anchored boxes, J. of Complexity 14 (1998), no. 4, 527–556.

    Article  Google Scholar 

  34. D. Mitchell, Ray Tracing and Irregularities of Distribution, Proc. 3rd Eurographics Workshop on Rendering (Bristol, UK), 1992, pp. 61–69.

    Google Scholar 

  35. H. Niederreiter, Quasirandom Sampling in Computer Graphics, Proc. 3rd Internat. Seminar on Digital Image Processing in Medicine, Remote Sensing and Visualization of Information (Riga, Latvia), 1992, pp. 29–34.

    Google Scholar 

  36. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.

    Google Scholar 

  37. H. Niederreiter, Error bounds for quasi-Monte Carlo integration with uniform point sets, J. Comput. Appl. Math. 150 (2003), 283–292.

    Article  MATH  MathSciNet  Google Scholar 

  38. A. Owen, Randomly Permuted (t, m, s)-Nets and (t, s)-Sequences, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, eds.), Lecture Notes in Statistics, vol. 106, Springer, 1995, pp. 299–315.

    Google Scholar 

  39. M. Pharr and G. Humphreys, Physically Based Rendering, Morgan Kaufmann, 2004.

    Google Scholar 

  40. M. Pauly, T. Kollig, and A. Keller, Metropolis Light Transport for Participating Media, Rendering Techniques 2000 (Proc. 11th Eurographics Workshop on Rendering) (B. Péroche and H. Rushmeier, eds.), Springer, 2000, pp. 11–22.

    Google Scholar 

  41. H. Press, S. Teukolsky, T. Vetterling, and B. Flannery, Numerical Recipes in C, Cambridge University Press, 1992.

    Google Scholar 

  42. M. Stamminger and G. Drettakis, Interactive Sampling and Rendering for Complex and Procedural Geometry, Rendering Techniques 2001 (Proc. 12th Eurographics Workshop on Rendering) (K. Myszkowski and S. Gortler, eds.), Springer, 2001, pp. 151–162.

    Google Scholar 

  43. P. Shirley, Discrepancy as a Quality Measure for Sampling Distributions, Eurographics’ 91 (Amsterdam, North-Holland), Elsevier Science Publishers, 1991, pp. 183–194.

    Google Scholar 

  44. I. Sloan and S. Joe, Lattice Methods for Multiple Integration, Clarendon Press, Oxford, 1994.

    Google Scholar 

  45. E. Veach, Robust Monte Carlo Methods for Light Transport Simulation, Ph.D. thesis, Stanford University, 1997.

    Google Scholar 

  46. J. Yellot, Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina, Science 221 (1983), 382–385.

    Google Scholar 

  47. S.K. Zaremba, La discrépance isotrope et l’intégration numérique, Ann. Mat. Pura Appl. 87 (1970), 125–136.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abt. Medieninformatik, University of Ulm, 89069, Ulm, Germany

    Alexander Keller

Authors
  1. Alexander Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

  2. INRIA Sophia Antipolis, route des lucioles 2004, 06902, Sophia Antipolis Cedex, France

    Denis Talay

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Keller, A. (2006). Myths of Computer Graphics. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_14

Download citation

Publish with us

Policies and ethics

Search

Navigation