On learning the visibility for joint importance sampling of low-order scattering

Volumetric path tracing relies on importance sampling to stochastically construct light transport paths from an emitter to the sensor. Existing techniques incrementally sample path vertices or segments with respect to the local scattering property incorporating the geometry and scattering terms. Thus the joint probability density for drawing a path results in a product of the conditional densities each for a local sampling decision. We present a joint path sampling technique that additionally accounts for the spatially varying visibility due to transmittance and occlusion along a double scattering path. The directional density is formulated as a Gaussian mixture model being fitted to single scattered radiance by the online expectation-maximization algorithm. It is first trained with samples oblivious to the visibility, then incrementally consumes an arbitrary number of samples being drawn from the actual scene. The resulting density in turn guides the directional sampling decision for both isotropic and anisotropic scattering. We demonstrate the benefit of our approach by integrating it into the unidirectional path tracing algorithm. The image noise is effectively reduced, even while rendering the heterogeneous participating media in the presence of complex opaque surfaces.