Primary-space Adaptive Control Variates Using Piecewise-polynomial Approximations

We present an unbiased numerical integration algorithm that handles both low-frequency regions and high-frequency details of multidimensional integrals. It combines quadrature Monte Carlo by using a quadrature-based approximation as control variate the signal. adaptively build constructed piecewise polynomial, which can be analytically integrated, accurately reconstructs integrand. then recover missed residual. Our work leverages importance sampling techniques working in primary space, allowing combination multiple mappings; this enables integration. is generic applied to any complex integral. demonstrate its effectiveness with four applications low dimensionality: transmittance estimation heterogeneous participating media, low-order scattering homogeneous direct illumination computation, rendering distribution effects. Finally, we show how our technique extensible integrands higher dimensionality computing on estimates high-dimensional signal, accounting for such additional residual well. In all cases, accurate results faster convergence compared previous approaches.