An error bound for decoupled visibility with application to relighting

Monte Carlo estimation of direct lighting is often dominated by visibility queries. If an error is tolerable, the calculations can be sped up by using a simple scalar occlusion factor per light source to attenuate radiance, thus decoupling the expensive estimation of visibility from the comparatively cheap sampling of unshadowed radiance and BRDF. In this paper we analyze the error associated with this approximation and derive an upper bound. We demonstrate in a simple relighting application how our result can be used to reduce noise by introducing a controlled error if a reliable estimate of the visibility is already available.