On Filtering the Noise from the Random Parameters in Monte Carlo Rendering

Monte Carlo (MC) rendering systems can produce spectacular images but are plagued with noise at low sampling rates. In this work, we observe that this noise occurs in regions of the image where the sample values are a direct function of the random parameters used in the Monte Carlo system. Therefore, we propose a way to identify MC noise by estimating this functional relationship from a small number of input samples. To do this, we treat the rendering system as a black box and calculate the statistical dependency between the outputs and inputs of the system. We then use this information to reduce the importance of the sample values affected by MC noise when applying an image-space, cross-bilateral filter, which removes only the noise caused by the random parameters but preserves important scene detail. The process of using the functional relationships between sample values and the random parameter inputs to filter MC noise is called Random Parameter Filtering (RPF), and we demonstrate that it can produce images in a few minutes that are comparable to those rendered with a thousand times more samples. Furthermore, our algorithm is general because we do not assign any physical meaning to the random parameters, so it works for a wide range of Monte Carlo effects, including depth of field, area light sources, motion blur, and path-tracing. We present results for still images and animated sequences at low sampling rates that have higher quality than those produced with previous approaches.