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Globally Adaptive Control Variate for Robust Numerical Integration

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.
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Anthony Pajot, Loic Barthe, Mathias Paulin. Globally Adaptive Control Variate for Robust Numerical Integration. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, vol. 36 (n° 4), pp. 1708-1730. ⟨10.1137/130937846⟩. ⟨hal-01118911⟩

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