“A progressive error estimation framework for photon density estimation”
Conference:
Type(s):
Title:
- A progressive error estimation framework for photon density estimation
Session/Category Title: Rendering
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We present an error estimation framework for progressive photon mapping. Although estimating rendering error has been established for unbiased rendering algorithms, error estimation for biased rendering algorithms has not been investigated well in comparison. We characterize the error by the sum of a bias estimate and a stochastic noise bound, which is motivated by stochastic error bounds formulation in biased methods. As a part of our error computation, we extend progressive photon mapping to operate with smooth kernels. This enables the calculation of illumination gradients with arbitrary accuracy, which we use to progressively compute the local bias in the radiance estimate. We also show how variance can be computed in progressive photon mapping, which is used to estimate the error due to noise. As an example application, we show how our error estimation can be used to compute images with a given error threshold. For this example application, our framework only requires the error threshold and a confidence level to automatically terminate rendering. Our results demonstrate how our error estimation framework works well in realistic synthetic scenes.
References:
1. Fiorio, C. V. 2004. Confidence intervals for kernel density estimation. Stata Journal 4, 2, 168–179(12).Google ScholarCross Ref
2. Geertsema, J. C. 1970. Sequential confidence intervals based on rank tests. The Annals of Mathematical Statistics 41, 3, 1016–1026.Google ScholarCross Ref
3. Glassner, A. S. 1995. Principles of Digital Image Synthesis. Morgan Kaufmann. Google ScholarDigital Library
4. Hachisuka, T., and Jensen, H. W. 2009. Stochastic progressive photon mapping. In SIGGRAPH Asia ’09: ACM SIGGRAPH Asia 2009 papers, ACM, New York, NY, USA, 1–8. Google ScholarDigital Library
5. Hachisuka, T., Ogaki, S., and Jensen, H. W. 2008. Progressive photon mapping. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2008) 27, 5, Article 130. Google ScholarDigital Library
6. Hastie, T., Tibshirani, R., and Friedman, J. 2001. The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., New York, NY, USA.Google Scholar
7. Havran, V., Bittner, J., Herzog, R., and Seidel, H.-P. 2005. Ray maps for global illumination. In Eurographics Symposium on Rendering, 43–54. Google ScholarDigital Library
8. Herzog, R., Havran, V., Kinuwaki, S., Myszkowski, K., and Seidel, H.-P. 2007. Global illumination using photon ray splatting. Computer Graphics Forum 26, 3, 503–513.Google ScholarCross Ref
9. Hey, H., and Purgathofer, W. 2002. Advanced radiance estimation for photon map global illumination. Computer Graphics Forum 21, 3.Google ScholarCross Ref
10. Jarosz, W., Zwicker, M., and Jensen, H. W. 2008. Irradiance Gradients in the Presence of Participating Media and Occlusions. Computer Graphics Forum (Proceedings of EGSR 2008) 27, 4, 1087–1096(10). Google ScholarDigital Library
11. Jensen, H. W. 2001. Realistic Image Synthesis Using Photon Mapping. A. K. Peters, Ltd., Natick, MA. Google ScholarDigital Library
12. Kajiya, J. T. 1986. The rendering equation. In Computer Graphics (SIGGRAPH ’86 Proceedings), D. C. Evans and R. J. Athay, Eds., vol. 20, 143–150. Google ScholarDigital Library
13. Lafortune, E. P., and Willems, Y. D. 1993. Bidirectional path tracing. In Proceedings of CompuGraphics, 95–104.Google Scholar
14. Lee, M. E., Redner, R. A., and Uselton, S. P. 1985. Statistically optimized sampling for distributed ray tracing. SIGGRAPH Comput. Graph. 19, 3, 61–68. Google ScholarDigital Library
15. Myszkowski, K. 1997. Lighting reconstruction using fast and adaptive density estimation techniques. In Proceedings of the Eurographics Workshop on Rendering Techniques ’97, Springer-Verlag, London, UK, 251–262. Google ScholarDigital Library
16. Perlin, K. 2002. Improving noise. In SIGGRAPH ’02: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 681–682. Google ScholarDigital Library
17. Purgathofer, W. 1987. A statistical method for adaptive stochastic sampling. Computer & Graphics, 11. Pergamon Press, New York.Google Scholar
18. Ramamoorthi, R., Mahajan, D., and Belhumeur, P. 2007. A first-order analysis of lighting, shading, and shadows. ACM Trans. Graph. 26, 1, 2. Google ScholarDigital Library
19. Ramasubramanian, M., Pattanaik, S. N., and Greenberg, D. P. 1999. A perceptually based physical error metric for realistic image synthesis. In SIGGRAPH ’99: Proceedings of the 26th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 73–82. Google ScholarDigital Library
20. Schregle, R. 2003. Bias compensation for photon maps. Comput. Graph. Forum 22, 4, 729–742.Google ScholarCross Ref
21. Silverman, B. 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York, NY.Google Scholar
22. Tamstorf, R., and Jensen, H. W. 1997. Adaptive smpling and bias estimation in path tracing. In Proceedings of the Eurographics Workshop on Rendering Techniques ’97, Springer-Verlag, London, UK, 285–296. Google ScholarDigital Library
23. Veach, E., and Guibas, L. J. 1995. Optimally combining sampling techniques for monte carlo rendering. In SIGGRAPH 95 Conference Proceedings, 419–428. Google ScholarDigital Library
24. Walter, B., Fernandez, S., Arbree, A., Bala, K., Donikian, M., and Greenberg, D. P. 2005. Lightcuts: a scalable approach to illumination. ACM Trans. Graph. 24, 3, 1098–1107. Google ScholarDigital Library
25. Walter, B. 1998. Density Estimation Techniques for Global Illumination. PhD thesis, Ithaca, NY, USA. Google ScholarDigital Library
26. Ward, G. J., and Heckbert, P. S. 1992. Irradiance gradients. Third Eurographics Workshop on Rendering, 8598.Google Scholar
27. Ward, G. J., Rubinstein, F. M., and Clear, R. D. 1988. A ray tracing solution for diffuse interreflection. In SIGGRAPH ’88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 85–92. Google ScholarDigital Library


