“Wavelet importance sampling: efficiently evaluating products of complex functions” by Clarberg, Jarosz, Akenine-Moller and Jensen

We present a new technique for importance sampling products of complex functions using wavelets. First, we generalize previous work on wavelet products to higher dimensional spaces and show how this product can be sampled on-the-fly without the need of evaluating the full product. This makes it possible to sample products of high-dimensional functions even if the product of the two functions in itself is too memory consuming. Then, we present a novel hierarchical sample warping algorithm that generates high-quality point distributions, which match the wavelet representation exactly. One application of the new sampling technique is rendering of objects with measured BRDFs illuminated by complex distant lighting — our results demonstrate how the new sampling technique is more than an order of magnitude more efficient than the best previous techniques.

1. Agarwal, S., Ramamoorthi, R., Belongie, S., and Jensen. H. W. 2003. Structured Importance Sampling of Environment Maps. ACM Transactions on Graphics 22, 3, 605–612. Google ScholarDigital Library
2. Burke, D., Ghosh. A., and Heidrich. W. 2004. Bidirectional Importance Sampling for Illumination from Environment Maps. In ACM SIGGRAPH Technical Sketches. Google ScholarDigital Library
3. Cabral. B., Max, N., and Springmeyer, R. 1987. Bidirectional Reflection Functions from Surface Bump Maps. In Computer Graphics (Proceedings of ACM SIGGRAPH 87), 273–281. Google ScholarDigital Library
4. Claustres, L., Paulin, M., and Boucher, Y. 2003. BRDF Measurement Modelling using Wavelets for Efficient Path Tracing. Computer Graphics Forum 22, 4, 701–716.Google ScholarCross Ref
5. Claustres, L., Boucher. Y., and Paulin, M. 2004. Wavelet Projection for Modelling of Acquired Spectral BRDF. Optical Engineering 43, 10, 2327–2339.Google ScholarCross Ref
6. Cohen, J., and Debevec, P., 2001. LightGen, HDRShop plugin. http://www.ict.usc.edu/ jcohen/lightgen/lightgen.html.Google Scholar
7. Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed Ray Tracing. In Computer Graphics (Proceedings of ACM SIGGRAPH 84), 137–145. Google ScholarDigital Library
8. Dana, K. J., Van Ginneken, B., Nayar, S. K., and Koenderink, J. J. 1999. Reflectance and Texture of Real-World Surfaces. ACM Transactions on Graphics 18, 1, 1–34. Google ScholarDigital Library
9. Debevec, P. 1998. Rendering Synthetic Objects into Real Scenes: Bridging Traditional and Image-Based Graphics with Global Illumination and High Dynamic Range Photography. In Proceedings of ACM SIGGRAPH 98, 189–198. Google ScholarDigital Library
10. Dutré, P., Bekaert, P., and Bala, K. 2003. Advanced Global Illumination. A K Peters. Google ScholarDigital Library
11. Jensen, H. W. 2001. Realistic Image Synthesis Using Photon Mapping. A K Peters. Google ScholarDigital Library
12. Kajiya, J. T. 1986. The Rendering Equation. In Computer Graphics (Proceedings of ACM SIGGRAPH 86), 143–150. Google ScholarDigital Library
13. Kollig, T., and Keller, A. 2003. Efficient Illumination by High Dynamic Range Images. In Eurographics Symposium on Rendering, 45–50. Google ScholarDigital Library
14. Lafortune, E. P., and Willems, Y. D. 1995. A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing. In Eurographics Workshop on Rendering, 11-20.Google Scholar
15. Lafortune, E. P. F., Foo, S.-C., Torrance, K. E., and Greenberg, D. P. 1997. Non-Linear Approximation of Reflectance Functions. In Proceedings of ACM SIGGRAPH 97, 117–126. Google ScholarDigital Library
16. Lalonde, P., and Fournier. A. 1999. Interactive Rendering of Wavelet Projected Light Fields. In Proceedings of Graphics Interface ’99, 107–114. Google ScholarDigital Library
17. Lalonde, P. 1997. Representations and Uses of Light Distribution Functions. PhD thesis, University of British Columbia. Google ScholarDigital Library
18. Lawrence, J., Rusinkiewicz. S., and Ramamoorthi. R. 2004. Efficient BRDF Importance Sampling using a Factored Representation. ACM Transactions on Graphics 23, 3, 496–505. Google ScholarDigital Library
19. Mallat, S. 1998. A Wavelet Tour of Signal Processing. Academic Press.Google Scholar
20. Matusik, W., Pfister, H., Brand, M. and McMillan, L. 2003. A Data-Driven Reflectance Model. ACM Transactions on Graphics 22, 3, 759–769. Google ScholarDigital Library
21. Miller, G. S. P., Rubin, S. M., and Ponceleon, D. B. 1998. Lazy Decompression of Surface Light Fields for Precomputed Global Illumination. In Eurographics Workshop on Rendering, 281–292.Google Scholar
22. Ng. R., Ramamoorthi R., and Hanrahan, P. 2004. Triple Product Wavelet Integrals for All-Frequency Relighting. ACM Transactions on Graphics 23, 3, 477-487. Google ScholarDigital Library
23. Niederreiter, H. 1992. Random Number Generation and Quasi-Monte Carlo Methods. Society for Industrial and Applied Mathematics. Google ScholarDigital Library
24. Ostromoukhov, V., Donohue, C., and Jodoin, P.-M. 2004. Fast Hierarchical Importance Sampling with Blue Noise Properties. ACM Transactions on Graphics 23, 3, 488–495. Google ScholarDigital Library
25. Pharr, M., and Humphreys. G. 2004. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann. Google ScholarDigital Library
26. Ramamoorthi, R., and Hanrahan, P. 2002. Frequency Space Environment Map Rendering. ACM Transactions on Graphics 21, 3, 517–526. Google ScholarDigital Library
27. Rusinkiewicz, S. M. 1998. A New Change of Variables for Efficient BRDF Representation. In Eurographics Workshop on Rendering, 11–22.Google ScholarCross Ref
28. Shirley, P. S. 1991. Physically Based Lighting Calculations for Computer Graphics. PhD thesis, University of Illinois at Urbana-Champaign. Google ScholarDigital Library
29. Stollnitz, E. J., Derose, T. D., and Salesin, D. H. 1996. Wavelets for Computer Graphics: Theory and Applications. Morgan Kaufmann. Google ScholarDigital Library
30. Veach, E., and Guibas, L. J. 1995. Optimally Combining Sampling Techniques for Monte Carlo Rendering. In Proceedings of ACM SIGGRAPH 95, 419–428. Google ScholarDigital Library
31. Ward, G. J. 1992. Measuring and Modeling Anisotropic Reflection. In Computer Graphics (Proceedings of ACM SIGGRAPH 92), 265–272. Google ScholarDigital Library