Table 2 Variances for multi-sample estimator for the four examples in Appendix C and the environment map example (× 10−3) for balance heuristic using equal count of samples, for the count inversely proportional to the variances of independent estimators [9] and [10], for the provably better, non-balance heuristic, estimator defined in [11], and for the three new estimators defined in this paper
From: Multiple importance sampling revisited: breaking the bounds
Ex. 1 | Ex. 2 | Ex. 3 | Ex. 4 | Ex. EM | |
\(\alpha _{k} \propto \frac {1}{n}\) | 29.16 | 4.91 | 10.68 | 28.14 | 4.63 |
24.11 | 4.55 | 2.02 | 330.85 | 1.47 | |
α k ∝σk,eq [11] | 29.09 | 4.90 | 10.61 | 27.94 | 4.61 |
\(\alpha _{k} \propto \frac {1}{m^{2}_{k}}\) | 26.55 | 4.77 | 0.37 | 809.28 | 3.16 |
α k ∝σk,eq | 29.90 | 4.99 | 9.48 | 6.61 | 4.36 |
α k ∝Mk,eq | 28.24 | 4.83 | 7.05 | 18.04 | 3.87 |