| Light transport algorithms generate realistic images by simulating the emission and scattering of light in an artificial environment. Applications include lighting design, architecture, and computer animation, while related engineering disciplines include neutron transport and radiative heat transfer. The main challenge with these algorithms is the high complexity of the geometric, scattering, and illumination models used. In this dissertation, we develop new Monte Carlo techniques that greatly extend the range of input models for which light transport simulations are practical.; We start by developing a rigorous theoretical basis for bidirectional light transport algorithms (those that combine direct and adjoint techniques). We propose a new formulation based on linear operators, such that for any physically valid input scene, the transport operators are symmetric. We also show how light transport can be formulated as an integral over a space of paths. This framework allows new sampling and integration techniques to be applied, such as the Metropolis sampling method.; Our statistical contributions include multiple importance sampling, a new variance reduction technique that can greatly increase the robustness of Monte Carlo integration. It uses more than one sampling technique to evaluate an integral, and combines these samples in a way that is provably close to optimal.; Finally, we propose new Monte Carlo light transport algorithms. Bidirectional path tracing uses a family of different path sampling techniques that generate some path vertices starting from a light source, and some starting from a sensor. We show that when these techniques are combined using multiple importance sampling, a large range of difficult lighting effects can be handled efficiently.; The second algorithm we describe is Metropolis light transport, inspired by the Metropolis sampling method from computational physics. Paths are generated by following a random walk through path space, such that the probability density of visiting each path is proportional the contribution it makes to the ideal image. The resulting algorithm is unbiased, handles arbitrary geometry and materials, and can be orders of magnitude more efficient than previous unbiased approaches for difficult lighting problems. To our knowledge, this is the first application of the Metropolis method to transport problems of any kind. |
