Geometric Sample Reweighting for Monte Carlo Integration

J. Guo; E. Eisemann

doi:10.1111/cgf.14405

Geometric Sample Reweighting for Monte Carlo Integration

J. Guo, E. Eisemann^*

^*Corresponding author for this work

Computer Graphics and Visualisation

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

111 Downloads (Pure)

Abstract

Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.

Original language	English
Pages (from-to)	109-119
Number of pages	11
Journal	Computer Graphics Forum
Volume	40
Issue number	7
DOIs	https://doi.org/10.1111/cgf.14405
Publication status	Published - 2021

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

CCS Concepts
Monte Carlo Integration
Rendering
Sample Reweighting
Sampling and Reconstruction
• Computing methodologies → Ray tracing

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10.1111/cgf.14405

cgf.14405Final published version, 24.4 MB

Cite this

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title = "Geometric Sample Reweighting for Monte Carlo Integration",

abstract = "Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.",

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author = "J. Guo and E. Eisemann",

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AU - Eisemann, E.

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PY - 2021

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N2 - Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.

AB - Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.

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KW - Monte Carlo Integration

KW - Rendering

KW - Sample Reweighting

KW - Sampling and Reconstruction

KW - • Computing methodologies → Ray tracing

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SP - 109

EP - 119

JO - Computer Graphics Forum

JF - Computer Graphics Forum

IS - 7

ER -

Geometric Sample Reweighting for Monte Carlo Integration

Abstract

Bibliographical note

Keywords

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Alternative Representations and Techniques for Accelerated Realistic Image Synthesis: Improved Sampling, Reconstruction and Modelling Methods

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