Adaptive Sampling for Monte Carlo Global Illumination Using Tsallis Entropy

  • Qing Xu
  • Shiqiang Bao
  • Rui Zhang
  • Ruijuan Hu
  • Mateu Sbert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3802)

Abstract

Adaptive sampling is an interesting tool to eliminate noise, which is one of the main problems of Monte Carlo global illumination algorithms. We investigate the Tsallis entropy to do adaptive sampling. Implementation results show that adaptive sampling based on Tsallis entropy consistently outperforms the counterpart based on Shannon entropy.

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References

  1. 1.
    Portes, M., Esquef, I.A., Gesualdi, A.R.: Image thresholding using Tsallis entropy. Pattern Recognition Letters 25, 1059–1065 (2004)CrossRefGoogle Scholar
  2. 2.
    Bekaert, P.: Hierarchical and Stochastic Algorithms for Radiosity. Ph.D. Dissertation, Katholieke Universiteit Leuven (December 1999)Google Scholar
  3. 3.
    Blahut, R.E.: Principles and Practice of Information Theory. Addison-Wesley, Boston (1987)MATHGoogle Scholar
  4. 4.
    Bolin, M.R., Meyer, G.W.: A perceptually based adaptive sampling algorithm. In: Cohen, M. (ed.) Proceedings SIGGRAPH 1998 Conference, Orlando, FL, USA, pp. 299–310 (1998)Google Scholar
  5. 5.
    Dippe, M.A.Z., Wold, E.H.: Antialiasing through Stochastic Sampling. Computer Graphics 19, 69–78 (1985)CrossRefGoogle Scholar
  6. 6.
    Philippe, J., Peroche, B.: A Progressive Rendering Algorithm Using an Adaptive Perceptually Based Image Metric. In: Cani, M.-P., Slater, M. (eds.) Proceedings of Eurographics 2004, INRIA and Eurographics Association (2004)Google Scholar
  7. 7.
    Guo, B.: Progressive Radiance Evaluation using Directional Coherence Maps. In: Cohen, M. (ed.) Proceedings of the SIGGRAPH 1998 Conference, Orlando, FL, USA, pp. 255–266 (1998)Google Scholar
  8. 8.
    Kirk, D., Arvo, J.: Unbiased variance reduction for global illumination. In: Brunet, P., Jansen, F.W. (eds.) Proceedings of the 2nd Eurographics Workshop on Rendering. Barcelona, pp. 153–156 (1991)Google Scholar
  9. 9.
    Kapur, J.N., Kesavan, H.K.: Entropy Optimization Principles with Applications. Academic Press, New York (1992)Google Scholar
  10. 10.
    Lee, M.E., Redner, R.A., Uselton, S.P.: Statistically Optimized Sampling for Distributed Ray Tracing. Computer Graphics 19, 61–65 (1985)CrossRefGoogle Scholar
  11. 11.
    Mitchell, D.P.: Generating Antialiased Images at Low Sampling Densities. Computer Graphics 21, 65–72 (1987)CrossRefGoogle Scholar
  12. 12.
    Pharr, M., Humphreys, G.: Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann, San Francisco (2004)Google Scholar
  13. 13.
    Painter, J., Sloan, K.: Antialiased Ray Tracing by Adaptive Progressive Refinement. Computer Graphics 23, 281–288 (1989)CrossRefGoogle Scholar
  14. 14.
    Purgathofer, W.: A Statistical Method for Adaptive Stochastic Sampling. Computers Graphics 11, 157–162 (1987)CrossRefGoogle Scholar
  15. 15.
    Renyi, A.: On measuresof entropy and information. Selected Papers of Alfred Renyi. 2, 525–580 (1976)Google Scholar
  16. 16.
    Rigau, J., Feixas, M., Sbert, M.: Entropy-based Adaptive Supersampling. In: Debevec, P., Gibson, S. (eds.) Proceedings of Thirteenth Eurographics Workshop on Rendering. Pisa, Italy (June 2002)Google Scholar
  17. 17.
    Rigau, J., Feixas, M., Sbert, M.: New Contrast Measures for Pixel Supersampling, pp. 439–451. Springer-Verlag London Limited, London (2002)Google Scholar
  18. 18.
    Rigau, J., Feixas, M., Sbert, M.: Entropy-based Adaptive Sampling. In: Proceedings of CGI 2003. IEEE Computer Society Press, Tokyo (2003)Google Scholar
  19. 19.
    Rigau, J., Feixas, M., Sbert, M.: Refinement Criteria Based on f-Divergences. In: Proceedings of Eurographics Symposium on Rendering 2003. Eurographics Association (2003)Google Scholar
  20. 20.
    Sharma, B.D., Autar, R.: An inversion theorem and generalized entropies for continuous distributions. SIAM J.Appl.Math. 25, 125–132 (1973)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Scheel, A., Stamminger, M., Putz, J., Seidel, H.: Enhancements to Directional Coherence Maps. In: Skala, V. (ed.) WSCG 2001 Proceedings of Ninth International Conference in Central Europeon Computer Graphics and Visualization. Plzen, Czech Republic, Plzen, February 5-9 (2001)Google Scholar
  22. 22.
    Santanna, A.P., Taneja, I.J.: Trigonometric entropies, Jensen difference divergence measures, and error bounds. Inf. Sci. 35, 145–156 (1985)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Smolikova, R., Wachowiak, M.P., Zurada, J.M.: An information-theoretic approach to estimating ultrasound backscatter characteristics. Computers in Biology and Medicine 34, 355–370 (2004)CrossRefGoogle Scholar
  24. 24.
    Tsallis, C., Albuquerque, M.P.: Are citations of scientific paper a case of nonextensivity. Euro. Phys. J. B 13, 777–780Google Scholar
  25. 25.
    Tamstorf, R., Jensen, H.W.: Adaptive Sampling and Bias Estimation in Path Tracing. In: Dorsey, J., Slusallek, P. (eds.) Rendering Techniques 1997, pp. 285–295. Springer, Heidelberg (1997)Google Scholar
  26. 26.
    Tsallis, C.: Possible generalization of Boltzmann-Gibbls statistics. Journal of Statistical Physics 52, 480–487 (1988)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Tatsuaki, W., Takeshi, S.: When nonextensive entropy becomes extensive. Physica A 301, 284–290Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Qing Xu
    • 1
  • Shiqiang Bao
    • 1
  • Rui Zhang
    • 1
  • Ruijuan Hu
    • 1
  • Mateu Sbert
    • 2
  1. 1.Department of Computer Science and TechnologyTianjin UniversityChina
  2. 2.Institute of Informatics and ApplicationsUniversity of GironaSpain

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