Information
- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: July 2001
- Number: TR-186-2-01-18
- Keywords: rendering equation, Monte-Carlo integration, importance sampling, Metropolis sampling
Abstract
The paper presents a new mutation strategy for the Metropolis
light transport algorithm, which works in
the space of uniform random numbers used to build up paths. Thus
instead of mutating directly in the path space, mutations are realized
in the infinite dimensional unit cube of pseudo-random numbers and these points are
transformed to the path space according to BRDF
sampling, light source sampling and Russian roulette.
This transformation makes the integrand and the importance
function flatter and thus increases the acceptance probability
of the new samples in the Metropolis algorithm. Higher
acceptance ratio,
in turn, reduces the correlation of the samples, which increases the
speed of convergence.
When mutations are calculated,
a new random point is selected usually in the neighborhood of the previous
one, but according to our proposition called ``large steps'',
sometimes an independent point is obtained.
Large steps greatly reduce the start-up bias and guarantee the ergodicity
of the process. Due to the fact that some samples are generated
independently of the previous sample, this method can also be
considered as a combination of the Metropolis algorithm with a
classical random walk. Metropolis light
transport is good in rendering bright image areas but poor in
rendering dark sections since it allocates samples proportionally
to the pixel luminance. Conventional random walks, on the other hand,
have the same performace everywhere, thus they are poorer than
Metropolis method in bright areas, but are better at dark sections.
In order to keep the merits of
both approaches, we use multiple importance sampling to combine
their results, that is, the combined method will be
as good at bright regions as Metropolis and
at dark regions as random walks.
The resulting scheme is robust, efficient, but most importantly,
is easy to implement and to combine with an available random-walk algorithm.
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BibTeX
@techreport{Szirmay-2001-METR,
title = "Simple and Robust Mutation Strategy for Metropolis Light
Transport Algorithm",
author = "Csaba Kelemen and L\'{a}szl\'{o} Szirmay-Kalos",
year = "2001",
abstract = "The paper presents a new mutation strategy for the
Metropolis light transport algorithm, which works in the
space of uniform random numbers used to build up paths. Thus
instead of mutating directly in the path space, mutations
are realized in the infinite dimensional unit cube of
pseudo-random numbers and these points are transformed to
the path space according to BRDF sampling, light source
sampling and Russian roulette. This transformation makes the
integrand and the importance function flatter and thus
increases the acceptance probability of the new samples in
the Metropolis algorithm. Higher acceptance ratio, in turn,
reduces the correlation of the samples, which increases the
speed of convergence. When mutations are calculated, a new
random point is selected usually in the neighborhood of the
previous one, but according to our proposition called
``large steps'', sometimes an independent point is obtained.
Large steps greatly reduce the start-up bias and guarantee
the ergodicity of the process. Due to the fact that some
samples are generated independently of the previous sample,
this method can also be considered as a combination of the
Metropolis algorithm with a classical random walk.
Metropolis light transport is good in rendering bright image
areas but poor in rendering dark sections since it allocates
samples proportionally to the pixel luminance. Conventional
random walks, on the other hand, have the same performace
everywhere, thus they are poorer than Metropolis method in
bright areas, but are better at dark sections. In order to
keep the merits of both approaches, we use multiple
importance sampling to combine their results, that is, the
combined method will be as good at bright regions as
Metropolis and at dark regions as random walks. The
resulting scheme is robust, efficient, but most importantly,
is easy to implement and to combine with
an available random-walk algorithm.",
month = jul,
number = "TR-186-2-01-18",
address = "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
institution = "Institute of Computer Graphics and Algorithms, Vienna
University of Technology ",
note = "human contact: technical-report@cg.tuwien.ac.at",
keywords = "rendering equation, Monte-Carlo integration, importance
sampling, Metropolis sampling",
URL = "https://www.cg.tuwien.ac.at/research/publications/2001/Szirmay-2001-METR/",
}