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Efficient Monte Carlo methods for light transport in scattering media


In this dissertation we focus on developing accurate and efficient Monte Carlo methods for synthesizing images containing general participating media. Participating media such as clouds, smoke, and fog are ubiquitous in the world and are responsible for many important visual phenomena which are of interest to computer graphics as well as related fields. When present, the medium participates in lighting interactions by scattering or absorbing photons as they travel through the scene. Though these effects add atmosphere and considerable depth to rendered images they are computationally very expensive to simulate. Most practical solutions make simplifying assumptions about the medium in order to maintain efficiency. Unfortunately, accurate and efficient simulation of light transport in general scattering media is a challenging undertaking. In this dissertation, we address this problem by introducing two complementary techniques. We first turn to the irradiance caching method for surface illumination. Irradiance caching gains efficiency by computing an accurate representation of lighting only at a sparse set of locations and reusing these values through interpolation whenever possible. We derive the mathematical concepts that form the foundation of this approach and analyze its strengths and weaknesses. Drawing inspiration from this algorithm, we then introduce a novel volumetric radiance caching method for efficiently simulating global illumination within participating media. In developing the technique we also introduce efficient methods for evaluating the gradient of the lighting within participating media. Our gradient analysis has immediate applicability for improved interpolation quality in both surface and media-based caching methods. We also develop a novel photon mapping technique for participating media. We present a theoretical reformulation of volumetric photon mapping, which provides significant new insights. This reformulation makes it easier to qualify the error introduced by the radiance estimate but, more importantly, also allows us to develop more efficient rendering techniques. Conventional photon mapping accelerate the computation of lighting at any point in the scene by performing density estimation. In contrast, our reformulation accelerates the computation of accumulated lighting along the length of entire rays. This algorithmic improvement provides for significantly reduced render times and even the potential for real-time visualization of light transport in participating media

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