| Authors | Eric Veach |
| Language | English |
| Type | public |
| Url | |
| Summary |
Light transport algorithms generate realistic images by simulating the
emission and scatter-ing 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 that are typically used. In this
disserta-tion, we develop new Monte Carlo techniques that greatly
extend the range of input models for which light transport simulations
are practical. Our contributions include new theoreti-cal models,
statistical methods, and rendering algorithms. We start by developing
a rigorous theoretical basis for bidirectional light transport
al-gorithms (those that combine direct and adjoint techniques). First,
we propose a linear op-erator formulation that does not depend on any
assumptions about the physical validity of the input scene. We show
how to obtain mathematically correct results using a variety of
bidirectional techniques. Next we derive a different formulation, such
that for any physi-cally valid input scene, the transport operators
are symmetric. This symmetry is important for both theory and
implementations, and is based on a new reciprocity condition that we
derive for transmissive materials. Finally, we show how light
transport can be formulated as an integral over a space of paths. This
framework allows new sampling and integration tech-niques to be
applied, such as the Metropolis sampling algorithm. We also use this
model to investigate the limitations of unbiased Monte Carlo methods,
and to show that certain kinds of paths cannot be sampled. Our
statistical contributions include a new technique called multiple
importance sam-pling, which can greatly increase the robustness of
Monte Carlo integration. It uses more than one sampling technique to
evaluate an integral, and then combines these samples in a
way that is provably close to optimal. This leads to estimators that
have low variance for a broad class of integrands. We also describe a
new variance reduction technique called efficiency-optimized Russian
roulette. Finally, we link these ideas together to obtain new Monte
Carlo light transport algo-rithms. 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 algorithm is unbiased, handles arbitrary
geometry and materials, and is relatively simple to implement. The
second algorithm we describe is Metropolis light transport, inspired
by the Me-tropolis 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 to the
contribution it makes to the ideal image. The resulting algorithm is
un-biased, uses little storage, handles arbitrary geometry and
materials, and can be orders of magnitude more efficient than previous
unbiased approaches. It performs especially well on problems that are
usually considered difficult, e.g. those involving bright indirect
light, small geometric holes, or glossy surfaces. To our knowledge,
this is the first application of the Metropolis method to transport
problems of any kind.
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| Pages | |
| Parts | Introduction
Monte Carlo Integration
Models for Bidirectional Light Transport in Computer
Graphics
Robust Light Transport Algorithms |
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