Separable Optimal Weights for Bidirectional Ray Tracing with Photon Maps while Mixing 3 Strategies

Abstract

Noise in the resultant image is inherent in the widely used bidirectional stochastic ray tracing with photon maps. The noise can be reduced by the Multiple Importance Sampling which combines results of different strategies with weights. In this paper we investigate the separable weights, derive and solve the system of integral equations that determine the optimal weights. It has several qualitative differences from the previously investigated case of general weights and results in more simple and numerically robust expressions. As before, they can be solved in the form of an algebraic formula that includes several integrals of the known functions that can be calculated in ray tracing. The integral terms entering those expressions are of primary importance and do not admit any simple heuristics but must be calculated accurately.