Tosato, Giovanna (2018) Hamiltonian Markov chains in light transport. [Magistrali biennali]
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The goal of rendering algorithms is to mimick the physical behavior of light as it is emitted from light sources, scattered by objects in the scene, and finally detected by a virtual sensor or camera. Classic Monte Carlo techniques used to solve the light transport problem, su ffer from long computation times, especially in high dimension where random walks result inefficient. Our idea is to exploit Hamiltonian dynamics to produce proposals for the Metropolis algoritm, so that it is not forced to stay in the local to have a good acceptance probability. We want to go beyond the current state of the art and construct an actual Markov chain that can follow the Hamiltonian flow at each step. Hamiltonian dynamics should follow the 'landscape' generated by the target function and drive samples avoiding the guess-and check strategy of a Random Walk that eventually will produce a slow or ine ffective exploration. Previous works have been done in this direction especially by Michael Betancourt and by Tzu-Mao Li et al., but the latter remains confi ned in the local, without deeply following Hamiltonian dynamics, since it follows it only for one step. What we aim with this thesis is to give a first theoretical analysis of the problem with an implementation attempt, setting ourselves into a volume, where potentially each light path is valid (assumption that is no longer true with geometry involved).
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