Markov chain Monte Carlo (MCMC) sampling is a powerful approach to generate samples from an arbitrary distribution. The application to light transport simulation allows us to efficiently handle complex light transport such as highly occluded scenes. Since light transport paths in MCMC methods are sampled according to the path contributions over the sampling domain covering the whole image, bright pixels receive more samples than dark pixels to represent differences in the brightness. This variation in the number of samples per pixel is a fundamental property of MCMC methods. This property often leads to uneven convergence over the image, which is a notorious and fundamental issue of any MCMC method to date. We present a novel stratification method of MCMC light transport methods. Our stratification method, for the first time, breaks the fundamental limitation that the number of samples per pixel is uncontrollable. Our method guarantees that every pixel receives a specified number of samples by running a single Markov chain per pixel. We rely on the fact that different MCMC processes should converge to the same result when the sampling domain and the integrand are the same. We thus subdivide an image into multiple overlapping tiles associated with each pixel, run an independent MCMC process in each of them, and then align all of the tiles such that overlapping regions match. This can be formulated as an optimization problem similar to the reconstruction step for gradient‐domain rendering. Further, our method can exploit the coherency of integrands among neighboring pixels via coherent Markov chains and replica exchange. Images rendered with our method exhibit much more predictable convergence compared to existing MCMC methods.

中文翻译：

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分层马尔可夫链蒙特卡罗轻型运输

马尔可夫链蒙特卡罗 (MCMC) 采样是一种从任意分布生成样本的强大方法。光传输模拟的应用使我们能够有效地处理复杂的光传输，例如高度遮挡的场景。由于 MCMC 方法中的光传输路径是根据覆盖整个图像的采样域上的路径贡献进行采样的，因此亮像素比暗像素接收更多样本以表示亮度差异。每像素样本数的这种变化是 MCMC 方法的基本属性。此属性通常会导致图像上的不均匀收敛，这是迄今为止任何 MCMC 方法的一个臭名昭著的基本问题。我们提出了一种新的 MCMC 光传输方法的分层方法。我们的分层方法，第一次，打破了每个像素的样本数量不可控的基本限制。我们的方法通过每个像素运行单个马尔可夫链来保证每个像素接收指定数量的样本。我们依赖于这样一个事实，即当采样域和被积函数相同时，不同的 MCMC 过程应该收敛到相同的结果。因此，我们将图像细分为与每个像素相关联的多个重叠图块，在每个图块中运行独立的 MCMC 过程，然后对齐所有图块以使重叠区域匹配。这可以表述为类似于梯度域渲染的重建步骤的优化问题。此外，我们的方法可以通过相干马尔可夫链和副本交换来利用相邻像素之间被积函数的相干性。