跳跃恢复光传输

Sascha Holl, Gurprit Singh, Hans-Peter Seidel
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引用次数: 0

摘要

当用传统方法从复杂的高维分布中采样困难重重时,马尔可夫链蒙特卡洛(MCMC)算法就派上用场了。尽管 MCMC 是一种功能强大的工具,但在实际应用中也很难控制和调整。同时实现对状态空间的局部探索和对目标分布的全局发现是一项艰巨的任务。在这项工作中,我们提出了一种 MCMC 方案,它包含了渲染中使用的所有现有 MCMC 采样器。然后,我们提出了一个新颖的框架,用于渲染{调整}任意马尔可夫链,使其对指定的目标分布表现出不变性。为了展示所提框架的潜力,我们将重点放在光传输模拟中的第一个简单应用上。作为副产品,我们将连续时间 MCMC 采样引入计算机图形学领域。我们展示了如何将任何现有的基于 MCMC 的光传输算法嵌入到我们的框架中。我们从经验和理论上证明,这种嵌入优于运行独立算法。事实上,我们的方法可以将任何现有算法转化为高度可并行化的变体,其运行时间更短、误差更小、方差更小。
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Jump Restore Light Transport
Markov chain Monte Carlo (MCMC) algorithms come to rescue when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in practice. Simultaneously achieving both \emph{local exploration} of the state space and \emph{global discovery} of the target distribution is a challenging task. In this work, we present a MCMC formulation that subsumes all existing MCMC samplers employed in rendering. We then present a novel framework for \emph{adjusting} an arbitrary Markov chain, making it exhibit invariance with respect to a specified target distribution. To showcase the potential of the proposed framework, we focus on a first simple application in light transport simulation. As a by-product, we introduce continuous-time MCMC sampling to the computer graphics community. We show how any existing MCMC-based light transport algorithm can be embedded into our framework. We empirically and theoretically prove that this embedding is superior to running the standalone algorithm. In fact, our approach will convert any existing algorithm into a highly parallelizable variant with shorter running time, smaller error and less variance.
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