Primary-space Adaptive Control Variates Using Piecewise-polynomial Approximations

Crespo, M. ; Jarabo, A. (Universidad de Zaragoza) ; Muñoz, A. (Universidad de Zaragoza)

Resumen: 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-based 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 distribution 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.

Idioma: Inglés

DOI: 10.1145/3450627

Año: 2021

Publicado en: ACM TRANSACTIONS ON GRAPHICS 40, 3 (2021), 25 [15 pp]
ISSN: 0730-0301

Factor impacto JCR: 7.403 (2021)

Categ. JCR: COMPUTER SCIENCE, SOFTWARE ENGINEERING rank: 9 / 110 = 0.082 (2021) - Q1 - T1

Factor impacto CITESCORE: 14.2 - Computer Science (Q1)

Factor impacto SCIMAGO: 7.148 - Computer Graphics and Computer-Aided Design (Q1)

Financiación: info:eu-repo/grantAgreement/EC/H2020/682080/EU/Intuitive editing of visual appearance from real-world datasets/CHAMELEON
Financiación: info:eu-repo/grantAgreement/ES/MINECO/PID2019-105004GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO/TIN2016-78753-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Lenguajes y Sistemas Inf. (Dpto. Informát.Ingenie.Sistms.)