Optimal sample weights for hemispherical integral quadratures

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  • dc.contributor.author Marques, Ricardoca
  • dc.contributor.author Bouville, Christianca
  • dc.contributor.author Bouatouch, Kadica
  • dc.date.accessioned 2018-04-25T09:36:36Z
  • dc.date.issued 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.identifier.citation Marques R, Bouville C, Bouatouch K. Optimal sample weights for hemispherical integral quadratures. Comput Graph Forum. 2018 Apr 10;38(1):59-72. DOI: 10.1111/cgf.13392
  • dc.identifier.doi http://dx.doi.org/10.1111/cgf.13392
  • dc.identifier.issn 1467-8659
  • dc.identifier.uri http://hdl.handle.net/10230/34455
  • dc.language.iso eng
  • dc.publisher Wileyca
  • dc.relation.ispartof Computer graphics forum. 2018 Apr 10;38(1):59-72
  • dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/707027
  • 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 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.
  • dc.rights.accessRights info:eu-repo/semantics/openAccess
  • dc.subject.keyword Monte Carlo techniques
  • dc.subject.keyword Global illumination
  • dc.subject.keyword Computing methodologies—Rendering
  • dc.subject.keyword Ray tracing
  • dc.title Optimal sample weights for hemispherical integral quadraturesca
  • dc.type info:eu-repo/semantics/article
  • dc.type.version info:eu-repo/semantics/acceptedVersion