Integral formulations of volumetric transmittance
Integral formulations of volumetric transmittance
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DOI：
10.1145/3355089.3356559
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发表时间：
2019-11
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通讯作者：
Iliyan Georgiev;Zackary Misso;T. Hachisuka;D. Nowrouzezahrai;Jaroslav Křivánek;Wojciech Jarosz
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文献类型：
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作者：
Iliyan Georgiev;Zackary Misso;T. Hachisuka;D. Nowrouzezahrai;Jaroslav Křivánek;Wojciech Jarosz
计算两个给定点之间的光衰减是体积光传输模拟中一项重要但昂贵的任务。现有的无偏透射率估计器均基于通过用虚构物质增强媒体而实现的“零散射”随机游走。这种公式阻止了传统蒙特卡洛估计方差分析的使用，因此此类方法的效率主要是从经验的角度来理解的。在本文中，我们提出了几种新颖的体积透射率积分公式，其中现有估计器作为直接蒙特卡罗估计器出现。打破物理直觉，我们表明零散射概念并不是无偏透射率估计所严格要求的，而是一种有效减少方差的控制变量形式。我们的公式为问题和现有估算器的效率带来了新的见解。它们还提供了一个用于设计新型透射率估计器的框架，该估计器具有独特且互补的性能权衡，以及应用样本分层的明确方法。
Computing the light attenuation between two given points is an essential yet expensive task in volumetric light transport simulation. Existing unbiased transmittance estimators are all based on "null-scattering" random walks enabled by augmenting the media with fictitious matter. This formulation prevents the use of traditional Monte Carlo estimator variance analysis, thus the efficiency of such methods is understood from a mostly empirical perspective. In this paper, we present several novel integral formulations of volumetric transmittance in which existing estimators arise as direct Monte Carlo estimators. Breaking from physical intuition, we show that the null-scattering concept is not strictly required for unbiased transmittance estimation, but is a form of control variates for effectively reducing variance. Our formulations bring new insight into the problem and the efficiency of existing estimators. They also provide a framework for devising new types of transmittance estimators with distinct and complementary performance tradeoffs, as well as a clear recipe for applying sample stratification.