Bibtex de la publication

@Article{ Pa2014.3,
author = {Pajot, Anthony and Barthe, Loïc and Paulin, Mathias},
title = "{Globally Adaptive Control Variate for Robust Numerical Integration}",
journal = {SIAM Journal on Scientific Computing},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
address = {},
year = {2014},
month = {août},
volume = {36},
number = {4},
pages = {1708--1730},
language = {anglais},
URL = { -},
keywords = {Numerical integration, Adaptive Monte-Carlo methods, Simulation and Modeling},
note = {},
abstract = {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 non-singular 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 non-singular 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 partic- ipating media voxelization application, which requires the computation of several millions integrals for complex media.}