Wavelet importance sampling: efficiently evaluating products of complex functions

1Lund University 2UC San Diego

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2005
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From left to right: BRDF importance sampling, environment map importance sampling, and importance sampling of the combination of BRDF and environment. With our new technique we can efficiently sample the product of the BRDF and the environment map without evaluating the full product. Sampling the product results in a superior sampling distribution (shown in the right image) compared with sampling the individual functions (shown on the left). 100 samples were used for each image. The BRDF is a measured acrylic blue material, shown for a single normal and viewing direction, and the environment map is Grace cathedral. Sample points for the product were generated in 0.1 milliseconds.
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Abstract

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.

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Petrik Clarberg, Wojciech Jarosz, Tomas Akenine-Möller, Henrik Wann Jensen. Wavelet importance sampling: efficiently evaluating products of complex functions. ACM Transactions on Graphics (Proceedings of SIGGRAPH), 24(3):1166–1175, August 2005. 
@article{clarberg05wavelet,
    author  = {Clarberg, Petrik and Jarosz, Wojciech and Akenine-M\"oller, Tomas and Jensen, Henrik Wann},
    title   = {Wavelet Importance Sampling: Efficiently Evaluating Products of Complex Functions},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
    volume  = {24},
    number  = {3},
    month   = aug,
    year    = {2005},
    pages   = {1166--1175},
    doi     = {10/c79g6q}
}
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