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Monte Carlo and Quasi-Monte Carlo Methods for Computer Graphics

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Monte Carlo and Quasi-Monte Carlo Methods 2006

Summary

Some computer graphics applications, such as architectural design, generate visually realistic images of computer models. This is accomplished by either explicitly or implicitly solving the light transport equations. Accurate solutions involve high-dimensional equations, and Monte Carlo (MC) techniques are used with an emphasis on importance sampling rather than stratification. For many applications, approximate solutions are adequate, and the dimensionality of the problem can be reduced. In these cases, the distribution of samples is important, and quasi-Monte Carlo (QMC) methods are often used. It is still unknown what sampling schemes are best for these lower dimensional graphics problems, or what “best” even means in this case. This paper reviews the work in MC and QMC computer graphics, and poses some open problems in the field.

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References

  1. A. Appel. Some techniques for shading machine rendering of solids. In Proceedings of the AFIPS 1968 Spring Joint Computer Conference, volume 32, pages 37–45, 1968.

    Google Scholar 

  2. J. Arvo. Stratified sampling of 2-manifolds. In SIGGRAPH Course: State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis, 2001.

    Google Scholar 

  3. S. Boulos, D. Edwards, J. D. Lacewell, J. Kautz, I. Wald, and P. Shirley. Packet-based whitted and distribution ray tracing. In Proceedings of Graphics Interface, 2007.

    Google Scholar 

  4. P. Christensen. Adjoints and importance in rendering: an overview. IEEE Transactions on Visualization and Computer Graphics, 9(3):329–340,2003.

    Article  Google Scholar 

  5. R. Cook. Stochastic sampling in computer graphics. ACM Transactions on Graphics, 5(1):51–72, 1986.

    Article  Google Scholar 

  6. R. Cook, T. Porter, and L. Carpenter. Distributed ray tracing. In Proceedings of SIGGRAPH, pages 165–174, 1984.

    Google Scholar 

  7. K. Chiu, P. Shirley, and C. Wang. Multi-jittered sampling. In Graphics gems IV, pages 370–374. Academic Press Professional, Inc., San Diego, CA, USA, 1994.

    Google Scholar 

  8. D. Cline, J. Talbot, and P. Egbert. Energy redistribution path tracing. In Proceedings of SIGGRAPH, pages 1186–1195, 2005.

    Google Scholar 

  9. P. Dutre, K. Bala, and P. Bekaert. Advanced Global Illumination. A. K. Peters, Ltd., Natick, Massachusetts, USA, second edition, 2006.

    Google Scholar 

  10. D. Dobkin, D. Eppstein, and D. Mitchell. Computing the discrepancy with applications to supersampling patterns. ACM Transactions on Graphics, 15(4):354–376, October 1996.

    Article  Google Scholar 

  11. D. Dobkin and D. Mitchell. Random-edge discrepancy of supersampling patterns. In Proceedings of Graphics Interface, pages 62–69, May 1993.

    Google Scholar 

  12. H. Faure. Good permutations for extreme discrepancy. J. Number Theory, 42:47–56, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Glassner. A model for fluorescence and phospherescence. In Proceedings of the EUROGRAPHICS rendering workshop, pages 57–68, 1994.

    Google Scholar 

  14. J. Gondek, G. Meyer, and J. Newman. Wavelength dependent reflectance functions. In Proceedings of SIGGRAPH, pages 213–220, 1994.

    Google Scholar 

  15. D. Greenberg, K. Torrance, P. Shirley, J. Arvo, J. Ferwerda, S. Pattanaik, E. Lafortune, B. Walter, S. Foo, and B. Trumbore. A framework for realistic image synthesis. In Proceedings of SIGGRAPH, pages 477–494, 1997.

    Google Scholar 

  16. S. Heinrich and A. Keller. Quasi-Monte Carlo methods in computer graphics, Part I: The QMC-Buffer. Technical Report 242/94, University of Kaiserslautern, Kaiserslautern, Germany, 1994.

    Google Scholar 

  17. S. Heinrich and A. Keller. Quasi-Monte Carlo methods in computer graphics, Part II: The radiance equation. Technical Report 243/94, University of Kaiserslautern, Kaiserslautern, Germany, 1994.

    Google Scholar 

  18. H. Wann Jensen. Realistic Image Synthesis Using Photon Mapping. A. K. Peters, Ltd., Natick, Massachusetts, USA, 2001.

    MATH  Google Scholar 

  19. H. Wann Jensen, S. Marschner, M. Levoy, and P. Hanrahan. A practical model for subsurface light transport. In Proceedings of SIGGRAPH, pages 511–518, 2001.

    Google Scholar 

  20. D. Kirk and J. Arvo. Unbiased variance reduction for global illumination. In Proceedings of the EUROGRAPHICS rendering workshop, 1991.

    Google Scholar 

  21. A. Keller. Quasi-Monte Carlo Methods for Photorealistic Image Synthesis. Ph.D. thesis, Shaker Verlag Aachen, 1998.

    Google Scholar 

  22. A. Keller. Strictly deterministic sampling methods in computer graphics. In SIGGRAPH Course: Monte Carlo Ray Tracing, 2003.

    Google Scholar 

  23. A. Keller. Stratification by rank-1 lattices. In Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 299–313, 2004.

    Google Scholar 

  24. A. Keller. Myths of computer graphics. In Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 217–244, 2006.

    Google Scholar 

  25. A. Keller and W. Heidrich. Interleaved sampling. In Proceedings of the EUROGRAPHICS rendering workshop, 2001.

    Google Scholar 

  26. T. Kollig and A. Keller. Efficient bidirectional path tracing by randomized Quasi-Monte Carlo integration. In Monte Carlo and Quasi-Monte Carlo Methods 2000, pages 290–305, 2002.

    Google Scholar 

  27. T. Kollig and A. Keller. Illumination in the presence of weak singularities. In Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 245–257, 2006.

    Google Scholar 

  28. C. Kolb, D. Mitchell, and P. Hanrahan. A realistic camera model for computer graphics. In Proceedings of SIGGRAPH, pages 317–324, 1995.

    Google Scholar 

  29. C. Kelemen, L. Szirmay-Kalos, G. Antal, and F. Csonka. A simple and robust mutation strategy for the Metropolis light transport algorithm. Computer Graphics Forum, 21(3):1–10, 2002.

    Article  Google Scholar 

  30. E. Lafortune and Y. Willems. Bi-directional path tracing. In Proceedings of Compugraphics, pages 145–153, 1993.

    Google Scholar 

  31. R. Morley, S. Boulos, J. Johnson, D. Edwards, P. Shirley, M. Ashikhmin, and S. Premože. Image synthesis using adjoint photons. In Proceedings of Graphics Interface, pages 179–186, 2006.

    Google Scholar 

  32. D. Mitchell. Spectrally optimal sampling for distribution ray tracing. In Proceedings of SIGGRAPH, pages 157–164, 1991.

    Google Scholar 

  33. D. Mitchell. Ray tracing and irregularities of distribution. In Proceedings of the EUROGRAPHICS rendering workshop, pages 61–70, 1992.

    Google Scholar 

  34. D. Mitchell. Quasirandom techniques. In SIGGRAPH Course: State of the art in Monte Carlo ray tracing for realistic image synthesis, 2001.

    Google Scholar 

  35. M. Mortenson. Geometric modeling. Industrial Press, New York, NY, USA, third edition, 2007.

    Google Scholar 

  36. R. Ohbuchi and M. Aono. Quasi-Monte Carlo rendering with adaptive sampling. Technical Report RT0167, IBM Tokyo Research Laboratory, November 1996.

    Google Scholar 

  37. S. Pattanaik. Computational Methods for Global Illumination and Visualisation of Complex 3D Environments. PhD thesis, Birla Inst. of Technology & Science, Pilani, India, 1993.

    Google Scholar 

  38. M. Pharr and G. Humphreys. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann Publishers, San Fransisco, California, USA, 2004.

    Google Scholar 

  39. M. Pauly, T. Kollig, and A. Keller. Metropolis light transport for participating media. In Proceedings of the EUROGRAPHICS rendering workshop, 2000.

    Google Scholar 

  40. E. Reinhard, G. Ward, S. Pattanaik, and P. Debevec. High Dynamic Range Imaging: Acquisition, Display and Image-Based Lighting. Morgan Kaufmann Publishers, San Francisco, CA, USA, 2005.

    Google Scholar 

  41. P. Shirley, M. Ashikhmin, M. Gleicher, S. Marschner, E. Reinhard, K. Sung, W. Thompson, and P. Willemsen. Fundamentals of Computer Graphics. A. K. Peters, Ltd., Natick, Massachusetts, USA, second edition, 2005.

    Google Scholar 

  42. P. Shirley and K. Chiu. A low distortion map between disk and square. journal of graphics tools, 2(3):45–52, 1997.

    Google Scholar 

  43. C. Schlick. An adaptive sampling technique for multidimensional ray tracing. In Proceedings of the EUROGRAPHICS rendering workshop, pages 48–56, 1991.

    Google Scholar 

  44. P. Shirley. Discrepancy as a quality measure for sample distributions. In Proceedings of EUROGRAPHICS, pages 183–194, 1991.

    Google Scholar 

  45. L. Szirmay-Kalos, B. Balazs, and M. Sbert. Metropolis iteration. In Proceedings of WSSG, 2004.

    Google Scholar 

  46. L. Szirmay-Kalos and W. Purgathofer. Analysis of the Quasi-Monte Carlo integration of the rendering equation. Technical Report TR-186-2-98-22, Vienna University of Technology, Vienna, Austria, 1998.

    Google Scholar 

  47. B. Smits and G. Meyer. Newton's colors: simulating interference phenomena in realistic image synthesis. In Proceedings of the EUROGRAPHICS rendering workshop, pages 185–194, 1990.

    Google Scholar 

  48. P. Shirley, K. Sung, and W. Brown. A ray tracing framework for global illumination systems. In Proceedings of Graphics Interface, pages 117–128, 1991.

    Google Scholar 

  49. J. Stam. Diffraction shaders. In Proceedings of SIGGRAPH, pages 101–110, 1999.

    Google Scholar 

  50. P. Shirley and C. Wang. Direct lighting calculation by Monte Carlo integration. In Proceedings of the EUROGRAPHICS rendering workshop, 1991.

    Google Scholar 

  51. J. Talbot. Importance resampling for global illumination. Master's thesis, Brigham Young University, Provo, Utah, USA, 2005.

    Google Scholar 

  52. E. Veach. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University, Stanford, California, USA, 1997.

    Google Scholar 

  53. E. Veach and L. Guibas. Bidirectional estimators for light transport. In Proceedings of the EUROGRAPHICS Rendering Workshop, pages 147–162, 1994.

    Google Scholar 

  54. E. Veach and L. Guibas. Metropolis light transport. In Proceedings of SIGGRAPH, pages 65–76, 1997.

    Google Scholar 

  55. B. Walter, P. Hubbard, P. Shirley, and D. Greenberg. Global illumination using local linear density estimation. ACM Transactions on Graphics, 16(3):217–259, 1997.

    Article  Google Scholar 

  56. A. Wilkie, R. Tobler, and W. Purgathofer. Combined rendering of polarization and fluorescence effects. In Proceedings of the EUROGRAPHICS rendering workshop, pages 197–204, 2001.

    Google Scholar 

  57. A. Wilkie, R. Tobler, C. Ulbricht, G. Zotti, and W. Purgathofer. An analytical model for skylight polarisation. In Proceedings of the EUROGRAPHICS Symposium on Rendering, pages 387–399, 2004.

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Utah, USA

    Peter Shirley, Dave Edwards & Solomon Boulos

Authors
  1. Peter Shirley
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  2. Dave Edwards
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  3. Solomon Boulos
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ulm University, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Alexander Keller

  2. Department of Computer Science, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Stefan Heinrich

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

    Harald Niederreiter

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Shirley, P., Edwards, D., Boulos, S. (2008). Monte Carlo and Quasi-Monte Carlo Methods for Computer Graphics. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_8

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