In Eric Veach of Stanford University’s dissertation Robust Monte Carlo Methods for Light Transport Simulation, he describes how newly developed Monte Carlo techniques can extend the range of input models for which light transport simulations are practical. This includes brand spanking new theoretical models, statistical methods and rendering algorithms. For the theoretical basis for bi-directional light transport Veach proposes a linear operator formulation, which does not assume anything about the physical validity of the input. Using bi-directional techniques, he shows how to get correct mathematical results. He then uses a different formulation, this time for any physically valid input such that the transport operators are symmetric. He finally shows how light transport can be formulated as and integral over a space of paths. This allows the new sampling and integration techniques to be applied and uses this model to look at the limitations of unbiased Monte Carlo methods and show that various kinds of paths cannot be sampled.

A new technique called multiple importance sampling greatly increases the robustness of Monte Carlo integration. To evaluate an integral, it uses more than one sampling technique and combines these samples in a way that is very close to optimal. Veach finally links all of these ideas together to get new Monte Carlo light transport algorithms. Once of these is the bi-directional path tracing that uses a family of different path sampling techniques and creates some path vertices starting from a from either a light source or a sensor. The algorithm is unbiased, handles arbitrary geometry and materials, and most importantly, it is simple to implement. The second algorithm is called metropolis light transport. This algorithm generates paths by following a random walk through path space so the probability of visiting each path is in proportion to the contribution it makes to the optimal image. This algorithm is also unbiased, it handles arbitrary geometry and materials, and more importantly it requires little storage and can be orders of magnititude more efficient than its predecessors.

This dissertation by Eric Veach of Stanford University has a little relationship with one of the techniques that we have been learning about in CS 322 Scientific Computing. We have learned the basic Monte Carlo integration technique and we see that here it is applied to a model that is used for light transportation simulation and used to create light transport algorithms that generate realistic images by simulating the emission and scattering of light in an artificial environment. There are many applications for which these algorithms are good for that include lighting design, architecture, and computer animation. Related engineering applications include neutron transport and radiative heat transfer. As we can see, the things that we learn in CS 322 are not a waste of our time but have useful applications in this world.