Variance reduction for Russian-roulette

László Szécsi, László Szirmay-Kalos, Csaba Kelemen
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Magyar Tudósok krt. 2, H-1117, HUNGARY


Russian-roulette is one of the most important techniques to compute infinite dimensional integrals in an unbiased way. However, Russian roulette is also responsible for adding large amount of noise. This paper examines Russian roulette and a related problem, the sampling of combined BRDFs and proposes two improvements that can reduce the additional noise of Russian-roulette and random elementary BRDF selection, keeping also the unbiasedness of the method. The first improvement takes advantage that the light transfer is computed on several wavelengths simultaneously, thus the distribution of the energy on the wavelengths should be more precisely taken into account when Russian-roulette is made to terminate the walk or to select randomly from the elementary BRDFs. The second improvement gets rid of the fundamental assumption of Russian roulette that the contribution is zero when the walk is terminated. If we have a better estimation for the incoming radiance at this case, this estimation can be used instead, which can significantly reduce the additional noise.

Keywords: Global illumination, random walks, Russian-roulette, spectral rendering, photon map