MIS Compensation: Optimizing Sampling Techniques in Multiple Importance Sampling

Abstract: Multiple importance sampling (MIS) has become an indispensable tool in Monte Carlo rendering, widely accepted as a near-optimal solution for combining different sampling techniques. But an MIS combination, using the common balance or power heuristics, often results in an overly defensive estimator, leading to high variance. We show that by generalizing the MIS framework, variance can be substantially reduced. Specifically, we optimize one of the combined sampling techniques so as to decrease the overall variance of the resulting MIS estimator. We apply the approach to the computation of direct illumination due to an HDR environment map and to the computation of global illumination using a path guiding algorithm. The implementation can be as simple as subtracting a constant value from the tabulated sampling density done entirely in a preprocessing step. This produces a consistent noise reduction in all our tests with no negative influence on run time, no artifacts or bias, and no failure cases.

Authors/Presenter(s): Ondřej Karlík, Chaos Czech a. s., Czech Republic
Martin Šik, Chaos Czech a. s., Czech Republic
Petr Vévoda, Charles University, Prague; Chaos Czech a. s., Czech Republic
Tomáš Skřivan, IST Austria, Czech Republic
Jaroslav Křivánek, Charles University, Prague; Chaos Czech a. s., Czech Republic

Variance-Aware Multiple Importance Sampling

Abstract: Many existing Monte Carlo methods rely on multiple importance sampling (MIS) to achieve robustness and versatility. Typically, the balance or power heuristics are used, mostly thanks to the seemingly strong guarantees regarding their variance. We show that these MIS heuristics are oblivious to the effect of certain variance reduction techniques like stratification. This shortcoming is particularly pronounced when unstratified and stratified techniques are combined (e.g., in a bidirectional path tracer). We propose to enhance the balance heuristic by injecting variance estimates. We achieve substantial variance reduction for combinations of stratified and unstratified techniques, as well as defensive sampling applications. The proposed method is simple to implement and introduces little overhead.

Authors/Presenter(s): Pascal Grittmann, Saarland University, Germany
Iliyan Georgiev, Autodesk, United Kingdom
Philipp Slusallek, DFKI, Saarland University, Germany
Jaroslav Krivanek, Charles University, Render Legion, Czech Republic

Selectively Metropolised Monte Carlo light transport simulation

Abstract: Light transport is a complex problem with many solutions. Practitioners are now faced with the difficult task of choosing which rendering algorithm to use for any given scene. Simple Monte Carlo methods, such as path tracing, work well for the majority of lighting scenarios, but introduce excessive variance when they encounter transport they cannot sample (such as caustics). More sophisticated rendering algorithms, such as bidirectional path tracing, handle a larger class of light transport robustly, but have a high computational overhead that makes them inefficient for scenes that are not dominated by difficult transport. The underlying problem is that rendering algorithms can only be executed indiscriminately on all transport, even though they may only offer improvement for a subset of paths. In this paper, we introduce a new scheme for selectively combining different Monte Carlo rendering algorithms. We use a simple transport method (e.g. path tracing) as the base, and treat high variance "fireflies" as seeds for a Markov chain that locally uses a Metropolised version of a more sophisticated transport method for exploration, removing the firefly in an unbiased manner. We use a weighting scheme inspired by MIS to partition the integrand into regions the base method can sample well and those it cannot, and only use Metropolis for the latter. This constrains the Markov chain to paths where it offers improvement, and keeps it away from regions already handled well by the base estimator. Combined with stratified initialization, short chain lengths and careful allocation of samples, this vastly reduces non-uniform noise and temporal flickering artifacts normally encountered with a global application of Metropolis methods. Through careful design choices, we ensure our algorithm never performs much worse than the base estimator alone, and usually performs significantly better, thereby reducing the need to experiment with different algorithms for each scene.

Authors/Presenter(s): Benedikt M. Bitterli, Dartmouth College, United States of America
Wojciech Jarosz, Dartmouth College, United States of America

Integral formulations of volumetric transmittance

Abstract: Computing the light attenuation between two given points is an essential yet expensive task in volumetric light transport simulation. Existing unbiased transmittance estimators are all based on "null-scattering" random walks enabled by augmenting the media with fictitious matter. This formulation prevents the use of traditional Monte Carlo estimator variance analysis, thus the efficiency of such methods is understood from a mostly empirical perspective. In this paper, we present several novel integral formulations of volumetric transmittance in which existing estimators arise as direct Monte Carlo estimators. Breaking from physical intuition, we show that the null-scattering concept is not strictly required for unbiased transmittance estimation, but is a form of control variates for effectively reducing variance. Our formulations bring new insight into the problem and the efficiency of existing estimators. They also provide a framework for devising new types of transmittance estimators with distinct and complementary performance tradeoffs, as well as a clear recipe for applying sample stratification.

Authors/Presenter(s): Iliyan Georgiev, Autodesk, United Kingdom
Zackary Misso, Dartmouth College, United States of America
Toshiya Hachisuka, The University of Tokyo, Japan
Derek Nowrouzezahrai, McGill University, Canada
Jaroslav Krivanek, Charles University, Render Legion, Czech Republic
Wojciech Jarosz, Dartmouth College, United States of America