We present an in-depth analysis of the sources of variance in state-of-the-art unbiased volumetric transmittance estimators, and propose several new methods for improving their efficiency. These combine to produce a single estimator that is universally optimal relative to prior work, with up to several orders of magnitude lower variance at the same cost, and has zero variance for any ray with non-varying extinction. We first reduce the variance of truncated power-series estimators using a novel efficient application of U-statistics. We then greatly reduce the average expansion order of the power series and redistribute density evaluations to filter the optical depth estimates with an equidistant sampling comb. Combined with the use of an online control variate built from a sampled mean density estimate, the resulting estimator effectively performs ray marching most of the time while using rarely-sampled higher order terms to correct the bias.

中文翻译：

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无偏射线行进透射率估计器

我们对最新的无偏体积透射率估算器中的方差源进行了深入分析，并提出了几种提高其效率的新方法。这些结合起来产生了一个相对于先前工作普遍最佳的单个估计量，同时以相同的成本将方差降低了几个数量级，并且对于具有不变消光的任何射线均具有零方差。我们首先使用U统计量的新颖有效应用来减少截断的幂级数估计量的方差。然后，我们大大降低了幂级数的平均展开阶数，并重新分配了密度评估，以等距采样梳对光学深度估计进行滤波。结合使用根据抽样的平均密度估算值构建的在线控制变量，