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绘制的重要组成部分，而真实感绘制又是计算机图形学的一个关键问题。在方差减小、鲁棒性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，这导致了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，即使是现代模拟方法也可能难以解决更具挑战性的运输问题，或者效率不够。其结果是不可预测的长计算时间或图像中的干扰残留误差或伪影（例如，在这个项目中，我们将利用对集成问题的理解，这已经沿着了上述的进步，来探索更强大的MC和MCMC方法的潜力，这些方法到目前为止在计算机图形学中还没有被探索过。一方面，我们将考虑多级蒙特卡罗方法，它使集成问题灵活地分裂成独立的估计量，我们将研究如何巧妙的分裂可以找到，如何总方差可以最小化（例如，通过灵活的资源分配或集成方案），以及如何分层集成可以最好地付诸实践。另一方面，我们将区域自适应马尔可夫链蒙特卡罗方法引入计算机图形学。应用于光传输模拟，他们使一个更灵活的路径突变策略的选择和控制的突变参数-也取决于马尔可夫链的状态和不同的选择概率的突变和变化的参数在一个单一的链。这导致了许多有趣的问题，例如，如何适当划分路径空间，或者如何导出并确保一致性和收敛性。同样出于这个原因，该项目进一步发展了该领域的一个当前主题，即新的（MC）MC方法。最近的工作激励使用数据驱动的方法来提高光传输模拟方法的效率。例如，可能在短的预处理模拟期间获得的关于运输的信息可以用于指导运输路径的构建。在这里，拟议的项目步骤，并将进行研究，如何因此所需的信息可以充分和更可靠地获得（例如，通过正规化的整合问题），到什么程度的数据需要存储（例如，存储传输路径或汇总统计），以及哪些数据表示和数据结构是非常适合存储和使用在模拟过程中。对于上述新方法，我们将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中的突变。

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.