Globally Adaptive Control Variate for Robust Numerical Integration

Many methods in computer graphics require the integration of functions on low-to-middle--dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration method, able to handle arbitrary nonsingular sca...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2014-01, Vol.36 (4), p.A1708-A1730
Main Authors: Pajot, Anthony, Barthe, Loïc, Paulin, Mathias
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computation
Computer Science
Computer Vision and Pattern Recognition
Graphics
Handles
Image Processing
Integrals
Mathematical analysis
Mathematical models
Monte Carlo methods
Numerical integration
Run time (computers)
Signal and Image Processing
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Summary:Many methods in computer graphics require the integration of functions on low-to-middle--dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration method, able to handle arbitrary nonsingular scalar or vector-valued functions defined on low-to-middle--dimensional spaces. Our method combines control variate, globally adaptive subdivision and Monte-Carlo estimation to achieve fast and accurate computations of any nonsingular integral. The runtime is linear with respect to standard deviation while standard Monte-Carlo methods are quadratic. We additionally show through numerical tests that our method is extremely stable from a computation time and memory footprint point of view, assessing its robustness. We demonstrate our method on a participating media voxelization application, which requires the computation of several millions integrals for complex media.
ISSN:1064-8275
1095-7197
DOI:10.1137/130937846