Global Importance Sampling of Glossy Surfaces Using the Photon Map

Importance sampling reduces the variance of Monte Carlo integration by focusing effort on the directions that contribute the most energy to the result. In this paper we present a computationally efficient global importance-sampling strategy. Final gather rays are generated in proportion to the product of all three factors of the rendering equation integrand: surface reflectance, incident radiance, and the cosine term. By focusing effort on those directions that contribute the most energy to the result, the variance is greatly reduced. To be suitable for an interactive system, the computational cost of generating samples and their associated probabilities must be low. Our method requires neither that the surface reflectance function be invertible, nor that an expensive calculation be performed after ray selection to evaluate the p.d.f. Building on Henrik Jensen's work, we use a photon map to estimate incident radiance. In this paper, we also use the photon map to render the final image. We compare our method to previous methods and conclude that our technique exhibits competitive variance reduction while requiring one fiftieth of the computation