Product Importance Sampling of the Volume Rendering Equation using Virtual Density Segments

Magnus Wrenninge, Ryusuke Villemin


We propose a new volumetric integration method that combines guiding of candidate point positions and importance resampling. We refer to this as the virtual density segment method (VDS). In particular, we show that this control can be driven by treating invertible PDFs as virtual density sources, which in turn steers a tracking algorithm to generate distributions of points that conform to the same, arbitrary PDFs. We combine this virtual density process with importance resampling to pick samples from the set of candidates according to the full product of the VRE. The resampling step is especially beneficial for non-invertible terms, such as complex light shapers like projected texture maps. In the end, by bridging tracking methods and inversion-based importance sampling, we arrive at a method for steering sampling that can incorporate any number of PDFs, thereby providing a general framework for combining arbitrary importance sampling schemes with tracking. Finally, having employed the importance resampling method for direct lighting, we also introduce a related method to the sampling of indirect volumetric illumination for highly anisotropic media.

Paper (PDF)

Available as Pixar Technical Memo #20-01