Efficient calculation of the optimal MIS weights in bidirectional ray tracing with photon maps

Bidirectional stochastic ray tracing (in particular, with photon maps) is well known technique for realistic computer graphics. However, its results are noisy, like all stochastic methods, which is clearly visible in the image. An approach called Multiple Importance Sampling can significantly reduce noise with the optimal weights used in it. In the paper we solved the partial optimization problem for mixing two strategies determined by the number of diffuse scattering events of the camera ray. Optimal weights that minimize noise obey an integral equation which can be solved in a closed form, and we present a numerical method to calculate its terms. It is based on Monte Carlo integration and stochastic ray tracing. The weights obtained in this way lead to noise reduction. The analysis of results for the test scene is presented.