Optimal sample weights for hemispherical integral quadratures

This paper proposes optimal quadrature rules over the hemisphere for the shading integral. We leverage recent work regarding the theory of quadrature rules over the sphere in order to derive a new theoretical framework for the general case of hemispherical quadrature error analysis. We then apply ou...

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Bibliographic Details
Authors: Marques, Ricardo, Bouville, Christian, Bouatouch, Kadi
Format: article
Status:Versión aceptada para publicación
Publication Date:2018
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/34455
Online Access:http://hdl.handle.net/10230/34455
http://dx.doi.org/10.1111/cgf.13392
Access Level:Open access
Keyword:Monte Carlo techniques
Global illumination
Computing methodologies—Rendering
Ray tracing
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spelling Optimal sample weights for hemispherical integral quadraturesMarques, RicardoBouville, ChristianBouatouch, KadiMonte Carlo techniquesGlobal illuminationComputing methodologies—RenderingRay tracingThis paper proposes optimal quadrature rules over the hemisphere for the shading integral. We leverage recent work regarding the theory of quadrature rules over the sphere in order to derive a new theoretical framework for the general case of hemispherical quadrature error analysis. We then apply our framework to the case of the shading integral. We show that our quadrature error theory can be used to derive optimal sample weights (OSW) which account for both the features of the sampling pattern and the material reflectance function (BRDF). Our method significantly outperforms familiar QMC and stochastic Monte Carlo techniques. Our results show that the OSW are very effective in compensating for possible irregularities in the sample distribution. This allows, for example, to significantly exceed the regular O(N-1=2) convergence rate of stochastic Monte Carlo while keeping the exact same sample sets. Another important benefit of our method is that OSW can be applied whatever the sampling points distribution: the sample distribution need not follow a probability density function, which makes our technique much more flexible than QMC or stochastic Monte Carlo solutions. In particular, our theoretical framework allows to easily combine point sets derived from different sampling strategies (e.g., targeted to diffuse and glossy BRDF). In this context our rendering results show that our approach overcomes MIS (Multiple Importance Sampling) techniques.Ricardo Marques was supported by the European Union’s Horizon 2020 research programme through a Marie Sklodowska-Curie Individual Fellowship (grant number 707027).Wiley20182018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/34455http://dx.doi.org/10.1111/cgf.13392reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésComputer graphics forum. 2018 Apr 10;38(1):59-72info:eu-repo/grantAgreement/EC/H2020/707027This is the peer reviewed version of the following article: Marques R, Bouville C, Bouatouch K. Optimal sample weights for hemispherical integral quadratures. Comput Graph Forum. 2018 Apr 10;38(1):59-72., which has been published in final form at http://dx.doi.org/10.1111/cgf.13392. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.info:eu-repo/semantics/openAccessoai:recercat.cat:10230/344552026-05-29T05:05:01Z
dc.title.none.fl_str_mv Optimal sample weights for hemispherical integral quadratures
title Optimal sample weights for hemispherical integral quadratures
spellingShingle Optimal sample weights for hemispherical integral quadratures
Marques, Ricardo
Monte Carlo techniques
Global illumination
Computing methodologies—Rendering
Ray tracing
title_short Optimal sample weights for hemispherical integral quadratures
title_full Optimal sample weights for hemispherical integral quadratures
title_fullStr Optimal sample weights for hemispherical integral quadratures
title_full_unstemmed Optimal sample weights for hemispherical integral quadratures
title_sort Optimal sample weights for hemispherical integral quadratures
dc.creator.none.fl_str_mv Marques, Ricardo
Bouville, Christian
Bouatouch, Kadi
author Marques, Ricardo
author_facet Marques, Ricardo
Bouville, Christian
Bouatouch, Kadi
author_role author
author2 Bouville, Christian
Bouatouch, Kadi
author2_role author
author
dc.subject.none.fl_str_mv Monte Carlo techniques
Global illumination
Computing methodologies—Rendering
Ray tracing
topic Monte Carlo techniques
Global illumination
Computing methodologies—Rendering
Ray tracing
description This paper proposes optimal quadrature rules over the hemisphere for the shading integral. We leverage recent work regarding the theory of quadrature rules over the sphere in order to derive a new theoretical framework for the general case of hemispherical quadrature error analysis. We then apply our framework to the case of the shading integral. We show that our quadrature error theory can be used to derive optimal sample weights (OSW) which account for both the features of the sampling pattern and the material reflectance function (BRDF). Our method significantly outperforms familiar QMC and stochastic Monte Carlo techniques. Our results show that the OSW are very effective in compensating for possible irregularities in the sample distribution. This allows, for example, to significantly exceed the regular O(N-1=2) convergence rate of stochastic Monte Carlo while keeping the exact same sample sets. Another important benefit of our method is that OSW can be applied whatever the sampling points distribution: the sample distribution need not follow a probability density function, which makes our technique much more flexible than QMC or stochastic Monte Carlo solutions. In particular, our theoretical framework allows to easily combine point sets derived from different sampling strategies (e.g., targeted to diffuse and glossy BRDF). In this context our rendering results show that our approach overcomes MIS (Multiple Importance Sampling) techniques.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/34455
http://dx.doi.org/10.1111/cgf.13392
url http://hdl.handle.net/10230/34455
http://dx.doi.org/10.1111/cgf.13392
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computer graphics forum. 2018 Apr 10;38(1):59-72
info:eu-repo/grantAgreement/EC/H2020/707027
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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