Adjoint-Driven Importance Sampling in Light Transport Simulation

Abstract

Monte Carlo light transport simulation has recently been adopted by the movie industry as a standard tool for producing photo realistic imagery. As the industry pushes current technologies to the very edge of their possibilities, the unprecedented complexity of rendered scenes has underlined a fundamental weakness of MC light transport simulation: slow convergence in the presence of indirect illumination. The culprit of this poor behaviour is that the sam- pling schemes used in the state-of-the-art MC transport algorithms usually do not adapt to the conditions of rendered scenes. We base our work on the ob- servation that the vast amount of samples needed by these algorithms forms an abundant source of information that can be used to derive superior sampling strategies, tailored for a given scene. In the first part of this thesis, we adapt general machine learning techniques to train directional distributions for biasing scattering directions of camera paths towards incident illumination (radiance). Our approach allows progressive training from a stream of particles while main- taining bounded memory footprint. This progressive nature makes the method robust even in scenarios where we have little information in the early stages of the training due to difficult visibility. The proposed method is not restricted only to path tracing, where paths start at the camera, but can be employed also in light tracing or photon mapping, where paths are emitted from light sources, as well as in combined bidirectional methods.

In the second part of this thesis we revisit Russian roulette and splitting, two vari- ance reduction techniques that have been used in computer graphics for more than 25 years. So far, however, the path termination (Russian roulette) and splitting rates have been based only on local material properties in the scene which can re- sult in inefficient simulation in the presence of indirect illumination. In contrast, we base the termination and splitting rates on a pre-computed approximation of the adjoint quantity (i.e. radiance in the case of path tracing) which yields superior results to previous approaches. To increase robustness of our method, we adopt the so called weight window, a standard technique in neutron transport simulations. Both methods, that is the biasing of scattering directions introduced in the first part of the thesis and the adjoint-driven Russian roulette and splitting, are based on the prior estimate of the adjoint quantity. Nevertheless, they consti- tute two complementary importance sampling strategies of transported light and as we show, their combination yields superior results to each strategy alone. As one of our contributions, we present a theoretical analysis that provides insights into the importance sampling properties of our adjoint-driven Russian roulette and splitting, and also explains the synergic behaviour of the two strategies.