Bidirectional stochastic ray tracing with photon maps is a powerful method but suffers from noise. It can be reduced by the Multiple Importance Sampling which combines results of different “strategies”. The “optimal weights” minimize the noise functional thus providing the best quality of the results. In the paper we derive and solve the system of integral equations that determine the optimal weights. It has several qualitative differences from the previously investigated case of mixing two strategies, but further increase of their number beyond 3 retains the qualitative features of the system. It can be solved in a closed form i.e. as an algebraic formula that include several integrals of the known functions that can be calculated in ray tracing.

stochastic ray tracing, photon maps, multiple importance sampling, optimal weights

Mathematical modelling in actual problems of science and technics

Ershov Sergey Valentinovich,  ,  orcid.org/0000-0002-5493-1076,  KIAM RAS

Kopylov Mikhail Sergeevich,  ,  orcid.org/0000-0002-9526-0766,  KIAM RAS

Voloboy Alexey Gennadievich,  ,  orcid.org/0000-0003-1252-8294,  KIAM RAS