Path Throughput Importance Weights

Many Monte Carlo light transport simulations use multiple importance sampling (MIS) to weight between different path sampling strategies. We propose to use the path throughput to compute the MIS weights instead of the commonly used probability density per area measure. This new formulation is equivalent to the previous approach and results in the same weights as well as implementation. However, it is more intuitive and can help in understanding the effects of modifications to the weight function. We show some examples of required modifications which are often neglected in implementations. Also, our new perspective might help to derive MIS strategies for new samplers in the future.Comment: 7 pages, 1 figur

Advances in Importance Sampling

Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm and the increase of the available computational resources have propelled the interest in this theoretically sound methodology. In this paper, we first describe the basic IS algorithm and then revisit the recent advances in this methodology. We pay particular attention to two sophisticated lines. First, we focus on multiple IS (MIS), the case where more than one proposal is available. Second, we describe adaptive IS (AIS), the generic methodology for adapting one or more proposals