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Optimal sample weights for hemispherical integral quadratures

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dc.contributor.author Marques, Ricardo
dc.contributor.author Bouville, Christian
dc.contributor.author Bouatouch, Kadi
dc.date.accessioned 2018-04-25T09:36:36Z
dc.date.issued 2018
dc.identifier.citation Marques R, Bouville C, Bouatouch K. Optimal sample weights for hemispherical integral quadratures. Comput Graph Forum. 2018. DOI: 10.1111/cgf.13392
dc.identifier.issn 1467-8659
dc.identifier.uri http://hdl.handle.net/10230/34455
dc.description Data de publicació electrònica:10-04-2018
dc.description.abstract 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.
dc.description.sponsorship Ricardo Marques was supported by the European Union’s Horizon 2020 research programme through a Marie Sklodowska-Curie Individual Fellowship (grant number 707027).
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Wiley
dc.rights This 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., 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.
dc.title Optimal sample weights for hemispherical integral quadratures
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1111/cgf.13392
dc.subject.keyword Monte Carlo techniques
dc.subject.keyword Global illumination
dc.subject.keyword Computing methodologies—Rendering
dc.subject.keyword Ray tracing
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/707027
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion
dc.embargo.liftdate 2019-04-10
dc.date.embargoEnd info:eu-repo/date/embargoEnd/2019-04-10

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