Arbitrary Importance Functions for Metropolis Light Transport

We present a generalization of the scalar importance function employed by Metropolis Light Transport (MLT) and related Markov chain rendering algorithms. Although MLT is known for its user-designable mutation rules, we demonstrate that its scalar contribution function is similarly programmable in an unbiased manner. Normally, MLT samples light paths with a tendency proportional to their brightness. For a range of scenes, we demonstrate that this importance function is undesirable and leads to poor sampling behaviour. Instead, we argue that simple user-designable importance functions can concentrate work in transport effects of interest and increase estimator efficiency. Unlike mutation rules, these functions are not encumbered with the calculation of transitional probabilities. We introduce alternative importance functions, which encourage the Markov chain to aggressively pursue sampling goals of interest to the user. In addition, we prove that these importance functions may adapt over the course of a render in an unbiased fashion. To that end, we introduce multi-stage MLT, a general rendering setting for creating such adaptive functions. This allows us to create a noise-sensitive MLT renderer whose importance function explicitly targets noise. Finally, we demonstrate that our techniques are compatible with existing Markov chain rendering algorithms and significantly improve their visual efficiency.