Primary-Space Adaptive Control Variates using Piecewise-Polynomial Approximations

08/15/2020
by   Miguel Crespo, et al.
0

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

READ FULL TEXT

page 2

page 3

page 4

page 5

page 6

page 7

page 8

page 14

research
12/21/2020

Spatial Monte Carlo Integration with Annealed Importance Sampling

Evaluating expectations on a pairwise Boltzmann machine (PBM) (or Ising ...
research
08/11/2018

Neural Importance Sampling

We propose to use deep neural networks for generating samples in Monte C...
research
08/05/2019

Geometric Sample Reweighting for Monte Carlo Integration

We present a general sample reweighting scheme and its underlying theory...
research
08/23/2018

Learning to Importance Sample in Primary Sample Space

Importance sampling is one of the most widely used variance reduction st...
research
05/02/2022

A Position-Free Path Integral for Homogeneous Slabs and Multiple Scattering on Smith Microfacets

We consider the problem of multiple scattering on Smith microfacets. Thi...
research
07/21/2023

Scenario Sampling for Large Supermodular Games

This paper introduces a simulation algorithm for evaluating the log-like...
research
11/22/2019

Importance Sampling of Many Lights with Reinforcement Lightcuts Learning

In this manuscript, we introduce a novel technique for sampling and inte...

Please sign up or login with your details

Forgot password? Click here to reset