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Citation: Abdalla Ahmed, Helene Perrier, David Coeurjolly, Victor Ostromoukhov, Jianwei Guo, Dongming Yan, Hui Huang, Oliver Deussen, Variance Analysis for Monte Carlo Integration, SIGGRAPH-ASIA 2016, ACM Trans. We use our framework to estimate the variance convergence rate of different state-of-the-art sampling patterns in both the Euclidean and spherical domains, as the number of samples increases. In this report, we revisit the work of Pilleboue et al.

Furthermore, we formulate design principles for constructing sampling methods that can be tailored according to available resources. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration.

We present a novel technique that produces two-dimensional low-discrepancy (LD) blue noise point sets for sampling.

Using one-dimensional binary van der Corput sequences, we construct two-dimensional LD point sets, and rearrange them to match a target spectral profile without loosing their low discrepancy. We propose a new spectral analysis of the variance in Monte Carlo integration, expressed in terms of the power spectra of the sampling pattern and the integrand involved.

For a new development flow or verification flow, validation procedures may involve modeling either flow and using simulations to predict faults or gaps that might lead to invalid or incomplete verification or development of a product, service, or system (or portion thereof, or set thereof).

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We store the rearrangement information in a compact lookup table that can be used to produce arbitrarily large point sets. We build our framework in the Euclidean space using Fourier tools and on the sphere using spherical harmonics.

We evaluate our technique and compare it to the state-of-the-art sampling approaches. We further provide a theoretical background that explains how our spherical framework can be extended to the hemispherical domain.

We validate our theoretical framework by performing numerical integration over several integrands sampled using different sampling patterns. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a more general theory.

Citation: Adrien Pilleboue, Gurprit Singh, David Coeurjolly, Michael Kazhdan, Victor Ostromoukhov, Variance Analysis for Monte Carlo Integration, SIGGRAPH 2015, ACM Trans. We review the related representation theory and show how it can be used to derive a closed-form solution. We introduce a novel fitting procedure that takes as input an arbitrary material, possibly anisotropic, and au- tomatically converts it to a microfacet BRDF.

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