Robust and Efficient Monte Carlo Light Transport Simulation using Regularizations and the Half Vector Integration Domain

Computer-generated imagery has become a central point in large and quickly growing areas such as computer animation, visual effects, architecture, high-quality visualization, and product design. A common requirement to all these areas is the efficient simulation of light transport from the light source to the sensor for image synthesis. This is a challenging task, as light can travel along all kinds of paths, and some paths are hard to find when computing the result numerically. The process of light propagation in a virtual scene is described by a path integral equation. This path integral is defined over the path space, the space of all possible light paths, on which photons travel from a light source to a virtual sensor. Monte Carlo approaches are employed for computing the path integral, where paths are stochastically generated (sampled). The integration, to compute an image of a virtual scene, in this space is challenging because of the mathematical properties of the integrand. In addition, the demand for both image quality and quantity requires shorter image rendering times, while imposing higher scene complexity at the same time. ... mehrWe provide several solutions to the problems arising with difficult light paths, especially these involving specular and glossy materials, as well as improve the rendering convergence with difficult illumination effects.
Some physical phenomena, such as perfectly specular reflection, cause singularities in the path integral, and thus are hard or even impossible to sample. We propose an approach to adaptively smooth difficult components of light transport, which makes them samplable while still ensuring convergence to the exact solution. It uses regularization for paths which cannot be sampled in an unbiased way. To introduce as little bias as possible, we selectively regularize individual interactions along paths, and also derive the regularization consistency conditions.
Additionally, in order to control the bias introduced by kernel smoothing, which is another means to sample complex light transport, we developed an adaptive bandwidth selection method. We have also analyzed the convergence rate for kernel smoothing methods in light transport.
On the other hand, even not perfectly specular, i.e., glossy, materials can be as difficult to sample. We propose a new way for representing light paths for more efficient exploration of the path space. Based on this, we propose a new mutation strategy, to be used with Markov chain Monte Carlo methods such as Metropolis light transport, which is well-suited for all configurations of surface scattering.
A different yet related problem is the creation of virtual scenes with photorealistic lighting. It can be challenging because it often requires interactive feedback and edits to the scene that are propagated consistently. To alleviate this process, we propose a set of visualization and manipulation tools, which allow the designers to grasp virtual illumination and to alter the physical laws of light transport for convenient illumination setup and analysis, as well as for achieving artistic goals.