Mr. Sergey Andreev Profile

Sergey Andreev

at MV Keldysh Institute of Applied Mathematics RAS

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Proceedings Article | 12 September 2021 Presentation + Paper

Optimal number of rays in bi-directional stochastic ray tracing with photon maps

Sergey Ershov, Alexey Voloboy, Sergey Andreev, Vladimir Galaktionov

Proceedings Volume 11874, 118740F (2021) https://doi.org/10.1117/12.2597172

KEYWORDS: Ray tracing, Stochastic processes, Monte Carlo methods, Computer simulations, Denoising, Visualization

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The traditional bi-directional stochastic ray tracing with photon maps (BDPM) is a popular method for physically accurate lighting simulation. Although it has been improved by application of MIS there are still problems such as the optimal number of rays. The implementation of the BDPM runs progressively, iteration by iteration, tracing a number of light and camera paths and then merging them. The noise achieved after a fixed rum time does not always decrease with the number of rays, so there is some optimum. We produce the method of calculating the optimal number of rays. Variance of the contribution to luminance calculated by BDPM in one iteration depends on the number of rays via a relatively simple algebraic law, yet more sophisticated then for classic Monte Carlo because the merged paths are not statistically independent in BDPM. The noise after the given simulation time is determined by this variance divided by the number of iteration done within that time, so the law includes the average time spent on tracing one light and one camera ray. Expectedly for the optimal number of camera paths the resulting noise is homogeneous over the image. One can make relative or absolute noise to be homogeneous so we have a single value for the whole image. The resulting formula includes “time per camera/light ray” only as a weighted sum over all pixels which can be easily measured from a single trial tracing. With this optimal choice the noise is reduced considerably.

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