Efficient and Robust Light Transport Simulation with adaptive (Markov Chain) Monte Carlo Methods

基于物理的光传输模拟是真实感渲染的重要组成部分，也是计算机图形学中的一个关键问题。在方差减小、鲁棒和高效的传输路径构建以及良好的分层方面的研究取得了巨大进展，导致蒙特卡罗和马尔可夫链蒙特卡罗方法（MC-和mcmc -方法）几乎完全用于模拟。然而，即使是现代的模拟方法也可能在更具有挑战性的运输问题上挣扎，或者根本不够有效。其结果是不可预测的长计算时间或图像中令人不安的残余误差或伪影（例如，在动画中可见的时间不稳定）。在这个项目中，我们将利用对集成问题的理解，随着上述进展而发展，探索更强大的MC-和mcmc -方法的潜力，这些方法目前在计算机图形学中尚未被探索。一方面，我们将考虑多级蒙特卡罗方法，它可以将集成问题灵活地分裂成独立的估计量，我们将研究如何找到聪明的分裂，如何最小化总方差（例如，通过灵活的资源分配或集成方案），以及如何将分层集成最好地付诸实践。另一方面，我们将引入区域自适应马尔可夫链蒙特卡罗方法到计算机图形学。应用于轻运输模拟，它们使更灵活的路径突变策略选择和突变参数控制——也取决于马尔可夫链的状态，以及单链内突变和参数的不同选择概率。这导致了许多有趣的问题，例如，路径空间的合适划分是什么样的，或者如何派生并确保一致性和收敛性。同样出于这个原因，本项目进一步发展了一个关于新（MC）MC-方法的领域的当前主题。最近的工作促使使用数据驱动的方法来提高光输运模拟方法的效率。例如，可能在短的预处理模拟期间获得的关于传输的信息可用于指导传输路径的构建。在这里，提议的项目介入并将研究如何充分和更可靠地获取所需的信息（例如，通过规范化集成问题），需要存储数据的程度（例如，存储传输路径或汇总统计数据），以及哪种数据表示和数据结构非常适合在模拟期间存储和使用。对于上述描述的新方法，我们将因此研究如何实现集成问题的数据驱动分裂或路径空间的划分，或者如何以数据驱动的方式控制自适应马尔可夫链的突变。

Physically-based light transport simulation is an integral part of photorealistic rendering, which in turn is a key problem in computer graphics. Great advances in research with regard to variance reduction, robust and efficient transport path construction, and good stratification led to an almost exclusive use of Monte Carlo and Markov Chain Monte Carlo-methods (MC- and MCMC-methods) for the simulation. However, even modern simulation methods can struggle, or are simply not efficient enough, with more challenging transport problems. The consequences are unpredictably long computation times or disturbing residual errors or artifacts in the images (e.g., visible as temporal instabilities in animations).In this project, we will leverage the understanding of the integration problem, which has evolved along with the aforementioned advances, to explore the potential of more powerful MC- and MCMC-methods which are up-to-now unexplored in computer graphics. On the one hand, we will consider Multi-Level Monte Carlo-methods, which enable a flexible splitting of the integration problem into independent estimators, and we will research how clever splittings can be found, how the total variance can be minimized (e.g. by flexible resource allocation or integration schemes), and how hierarchical integration can be best put into practice. On the other hand, we will introduce regional-adaptive Markov Chain Monte Carlo-methods to computer graphics. Applied to light transport simulation, they enable a more flexible path mutation strategy selection and control of mutation parameters -- also depending on the state of Markov chains and with varying selection probabilities of mutations and varying parameters within a single chain. This leads to numerous interesting questions, for example, how a suitable partitioning of the path space looks like, or how one derives and ensures the properties of consistency and convergence. Also for this reasons, this project further develops a current topic in the field with regard to the new (MC)MC-methods. Recent work motivates the use of data-driven approaches to improve the efficiency of light transport simulation methods. For example, information on the transport, possibly acquired during a short preprocess-simulation, can be used to guide the construction of transport paths. Here the proposed project steps in and will conduct research on how the therefor required information can be acquired sufficiently and more reliably (e.g. through regularizing the integration problem), to what extent data needs to be stored (e.g. storing transport paths or aggregate statistics), and which data representations and data structures are well suited for storage and usage during simulation. For the above described new methods we will thereby research how data-driven splitting of the integration problem or partitioning of the path space can be achieved, or how mutations in adaptive Markov chains can be controlled in a data driven fashion.