Orthogonal Array Sampling for Monte Carlo Rendering
Orthogonal Array Sampling for Monte Carlo Rendering
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DOI：
10.1111/cgf.13777
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发表时间：
2019-07
影响因子：
2.5
通讯作者：
Wojciech Jarosz;Afnan Enayet;Andrew E. Kensler;Charlie Kilpatrick;Per H. Christensen
中科院分区：
文献类型：
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作者：
Wojciech Jarosz;Afnan Enayet;Andrew E. Kensler;Charlie Kilpatrick;Per H. Christensen
我们通过引入和改进统计文献中称为正交阵列的一类技术，将N - rooks，抖动和（相关）多抖动采样推广到更高的维度。渲染器通常结合或“填充”一组低维（例如2D和1D）分层模式，形成高维样本进行集成。这保持了原始维度对中的分层，但失去了所有其他维度对的分层。对于真正的多维积分，如渲染中的那些，这增加了方差，并降低了其收敛速度到纯随机抽样的速度。因此，必须小心地将主要维度对分配给具有最多可积变量的维度，但这会使实现变得复杂。我们通过开发一组实用的、原位的多维样本生成例程来解决这个问题，这些例程可以同时对所有t维和1维投影上的点进行分层。例如，当t=2时，我们样本的任何2D投影都是一个（相关的）多抖动点集。这种特性不仅减少了方差，而且简化了实现，因为现在可以在保持相同分层水平的同时任意地将样本维度分配给被积维度。与传统的二维填充方法(如PBRT的（0,2）和分层采样器相比，我们的技术减少了方差，并提供了与Sobol和Halton等最先进的QMC采样器几乎相同的质量，同时避免了使用单个样本集覆盖整个图像时常见的结构化伪影。虽然在这项工作中，我们专注于构建有限采样点集，但我们也讨论了将来将我们的工作扩展到渐进序列（更适合增量渲染）的潜在途径。
We generalize N‐rooks, jittered, and (correlated) multi‐jittered sampling to higher dimensions by importing and improving upon a class of techniques called orthogonal arrays from the statistics literature. Renderers typically combine or “pad” a collection of lower‐dimensional (e.g. 2D and 1D) stratified patterns to form higher‐dimensional samples for integration. This maintains stratification in the original dimension pairs, but looses it for all other dimension pairs. For truly multi‐dimensional integrands like those in rendering, this increases variance and deteriorates its rate of convergence to that of pure random sampling. Care must therefore be taken to assign the primary dimension pairs to the dimensions with most integrand variation, but this complicates implementations. We tackle this problem by developing a collection of practical, in‐place multi‐dimensional sample generation routines that stratify points on all t‐dimensional and 1‐dimensional projections simultaneously. For instance, when t=2, any 2D projection of our samples is a (correlated) multi‐jittered point set. This property not only reduces variance, but also simplifies implementations since sample dimensions can now be assigned to integrand dimensions arbitrarily while maintaining the same level of stratification. Our techniques reduce variance compared to traditional 2D padding approaches like PBRT's (0,2) and Stratified samplers, and provide quality nearly equal to state‐of‐the‐art QMC samplers like Sobol and Halton while avoiding their structured artifacts as commonly seen when using a single sample set to cover an entire image. While in this work we focus on constructing finite sampling point sets, we also discuss potential avenues for extending our work to progressive sequences (more suitable for incremental rendering) in the future.