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

点击翻译按钮获取中文摘要

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.