Error analysis of estimators that use combinations of stochastic sampling strategies for direct illumination
Error analysis of estimators that use combinations of stochastic sampling strategies for direct illumination
复制标题
使用直接照明随机采样策略组合的估计器的误差分析
DOI：
10.1111/cgf.12416
复制
发表时间：
2014
影响因子：
2.5
通讯作者：
Kenny Mitchell
中科院分区：
文献类型：
--
作者：
Kartic Subr;D. Nowrouzezahrai;Wojciech Jarosz;J. Kautz;Kenny Mitchell
本文对蒙特卡罗估计组合在图像合成中的误差进行了理论分析。重要性抽样和多重重要性抽样是常用的方差减小策略。不幸的是，这两种策略都不能提高蒙特卡洛积分的收敛速度。另一方面，抖动采样（一种分层采样）可以提高收敛速度。大多数渲染软件都乐观地将重要性采样与抖动采样结合起来，希望两者都能实现。给出了多重重要采样与抖动采样相结合的精确误差。此外，我们还证明了在收敛速率估计之间引入负相关（反采样）的进一步好处。与重要性抽样一样，已知对偶抽样可以在不影响收敛速度的情况下减少某些类别的被积的误差。在本文中，我们的分析和实验表明，如果明智地使用重要性和对偶采样，并与抖动采样相结合，可以提高收敛速度。我们展示了这种策略组合对直接照明估计器收敛速率的影响。
We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance‐reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination.