Globally Adaptive Control Variate for Robust Numerical Integration
Anthony Pajot, Loïc Barthe, Mathias Paulin · SIAM Journal on Scientific Computing · 2014
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.