2020/08/15 by Miguel Crespo, Crespo, Miguel, Felix Bernal +5 · 1 citation
Computer Science · Medicine · #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences #Graphics (cs.GR) #Image and Signal Denoising Methods #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2008.06722
openalex publication_date 2020/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an unbiased numerical integration algorithm that handles both\nlow-frequency regions and high frequency details of multidimensional integrals.\nIt combines quadrature and Monte Carlo integration, by using a quadrature-base\napproximation as a control variate of the signal. We adaptively build the\ncontrol variate constructed as a piecewise polynomial, which can be\nanalytically integrated, and accurately reconstructs the low frequency regions\nof the integrand. We then recover the high-frequency details missed by the\ncontrol variate by using Monte Carlo integration of the residual. Our work\nleverages importance sampling techniques by working in primary space, allowing\nthe combination of multiple mappings; this enables multiple importance sampling\nin quadrature-based integration. Our algorithm is generic, and can be applied\nto any complex multidimensional integral. We demonstrate its effectiveness with\nfour applications with low dimensionality: transmittance estimation in\nheterogeneous participating media, low-order scattering in homogeneous media,\ndirect illumination computation, and rendering of distributed effects. Finally,\nwe show how our technique is extensible to integrands of higher dimensionality,\nby computing the control variate on Monte Carlo estimates of the\nhigh-dimensional signal, and accounting for such additional dimensionality on\nthe residual as well. In all cases, we show accurate results and faster\nconvergence compared to previous approaches.\n