Multiple importance sampling revisited: breaking the bounds

• Published in: EURASIP journal on advances in signal processing Vol. 2018; no. 1; pp. 1 - 15
• Main Authors: Sbert, Mateu, Havran, Vlastimil, Szirmay-Kalos, Laszlo
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.02.2018; Springer; SpringerOpen
• Subjects: Engineering; Global illumination; Monte Carlo; Multiple importance sampling; Quantum Information Technology; Rendering equation analysis; Signal,Image and Speech Processing; Spintronics; Monte Carlo; Global illumination; Rendering equation analysis; Multiple importance sampling; secondary Computer Graphics G.3 Mathematics of Computing / PROBABILITY AND STATISTICS probabilistic algorithms; primary Computer Graphics G.3 Mathematics of Computing/PROBABILITY AND STATISTICS probabilistic algorithms; Computer Graphics G.3 Mathematics of Computing / PROBABILITY AND STATISTICS probabilistic algorithms
• ISSN: 1687-6180; 1687-6180
• DOI: 10.1186/s13634-018-0531-2

We revisit the multiple importance sampling (MIS) estimator and investigate the bound on the efficiency improvement over balance heuristic estimator with equal count of samples established in Veach’s thesis. We revise the proof for this and come to the conclusion that there is no such bound and henceforth it makes sense to look for new estimators that improve on balance heuristic estimator with equal count of samples. Next, we examine a recently introduced non-balance heuristic MIS estimator that is provably better than balance heuristic with equal count of samples, and we improve it both in variance and efficiency. We then obtain an equally provably better one-sample balance heuristic estimator, and finally, we introduce a heuristic for the count of samples that can be used when the individual techniques are biased. All in all, we present three new sampling strategies to improve on both variance and efficiency on the balance heuristic using non-equal count of samples. Our scheme requires the previous knowledge of several quantities, but those can be obtained in an adaptive way. The results also show that by a careful examination of the variance and properties of the estimators, even better estimators could be discovered in the future. We present examples that support our theoretical findings.