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Efficient quadrature rules for illumination integrals : from quasi Monte Carlo to Bayesian Monte Carlo

Author: Ricardo Marques; C Bouville; Luis Paulo Santos; K Bouatouch
Publisher: San Rafael, California : Morgan & Claypool Publishers, [2015]
Series: Synthesis lectures in computer graphics and animation, #19.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Rendering photorealistic images is a costly process which can take up to several days in the case of high quality images. In most cases, the task of sampling the incident radiance function to evaluate the illumination integral is responsible for an important share of the computation time. Therefore, to reach acceptable rendering times, the illumination integral must be evaluated using a limited set of samples. Such  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ricardo Marques; C Bouville; Luis Paulo Santos; K Bouatouch
ISBN: 9781627057707 1627057706
OCLC Number: 911246019
Notes: Part of: Synthesis digital library of engineering and computer science.
Description: 1 online resource (x, 82 pages) : illustrations.
Contents: 1. Introduction --
1.1 The global illumination problem --
1.2 Illumination integral evaluation --
1.3 Motivation --
1.4 Book overview. 2. Spherical Fibonacci point sets for QMC estimates of illumination integrals --
2.1 Introduction --
2.2 Background --
2.2.1 QMC on the unit square --
2.2.2 QMC rules on the unit spherE --
2.2.3 QMC point sets --
2.2.4 Hemispherical projections --
2.2.5 Summary --
2.3 Spherical Fibonacci point sets --
2.4 QMC for illumination integrals --
2.5 Results --
2.5.1 Experimental setup --
2.5.2 Predicting the estimate error --
2.5.3 Experimental estimate error --
2.6 Conclusion. 3. Bayesian Monte Carlo for global illumination --
3.1 Introduction and motivation --
3.2 Representing a function using a smooth model --
3.2.1 Linear basis functions model --
3.2.2 Bayesian regression --
3.3 Bayesian Monte Carlo --
3.3.1 BMC quadrature equations --
3.3.2 Reducing the number of hyperparameters --
3.3.3 Summary --
3.4 Applying BMC to global illumination --
3.4.1 Spherical Gaussians for fast quadrature computation --
3.4.2 Prior GP: a global model with local adaptation --
3.4.3 Optimal samples set for illumination integrals --
3.4.4 From the hemisphere to the Gaussian lobe --
3.4.5 Precomputations --
3.4.6 The rendering algorithm --
3.5 Results --
3.5.1 Experimental environment --
3.5.2 Hyperparameters learning --
3.5.3 Comparison: BMC vs. QMC --
3.5.4 Skipping the learning step --
3.6 Conclusion. A. Posterior distribution --
Bibliography --
Authors' biographies.
Series Title: Synthesis lectures in computer graphics and animation, #19.
Responsibility: Ricardo Marques, Christian Bouville, Luís Paulo Santos, Kadi Bouatouch.

Abstract:

Rendering photorealistic images is a costly process which can take up to several days in the case of high quality images. In most cases, the task of sampling the incident radiance function to evaluate the illumination integral is responsible for an important share of the computation time. Therefore, to reach acceptable rendering times, the illumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. One must thus ensure that sampling produces the highest amount of information possible by carefully placing and weighting the limited set of samples. Furthermore, the integral evaluation should take into account not only the information brought by sampling but also possible information available prior to sampling, such as the integrand smoothness. This idea of sparse information and the need to fully exploit the little information available is present throughout this book. The presented methods correspond to the state-of-the-art solutions in computer graphics, and take into account information which had so far been underexploited (or even neglected) by the previous approaches. The intended audiences are Ph. D. students and researchers in the field of realistic image synthesis or global illumination algorithms, or any person with a solid background in graphics and numerical techniques.

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