Evaluation of three Monte Carlo estimation schemes for flux at a point

Kalli, H.; Cashwell, E.D.

doi:10.2172/7280869

Cited by 14 publications

(12 citation statements)

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“…Note that this PDF is exactly equal to that of equiangular sampling [Kalli and Cashwell 1977;Rief et al 1984;Kulla and Fajardo 2012] provided a, ω cb , and c are given.…”

Section: Unidirectional Factorization Pdfsmentioning

confidence: 96%

“…To remedy this problem, he proposed the once collided flux (OCF) estimator-which samples an extra path vertex when forming the connection-and proved that this strategy reduces the order of the singularity to 1/r and recovers the more favorable 1/ √ N convergence rate. Since this seminal work, many researchers have suggested improvements or simplifications to the OCF [Steinberg and Kalos 1971;Kalli and Cashwell 1977;Rief et al 1984;Raab and Beikert 1999]. Notable examples include the use of an equiangular approach (similar to Kulla and Fajardo's [2012]) to sample the extra vertex [Kalli and Cashwell 1977;Rief et al 1984].…”

Section: Related Workmentioning

confidence: 99%

“…Since this seminal work, many researchers have suggested improvements or simplifications to the OCF [Steinberg and Kalos 1971;Kalli and Cashwell 1977;Rief et al 1984;Raab and Beikert 1999]. Notable examples include the use of an equiangular approach (similar to Kulla and Fajardo's [2012]) to sample the extra vertex [Kalli and Cashwell 1977;Rief et al 1984]. Much like Kalos' OCF estimator and its extensions, we sample additional path vertices to reduce singularities; however, we go a step further by considering not just one but two vertices, while also accounting for all geometry terms and anisotropic phase functions along the connecting subpath.…”

Section: Related Workmentioning

confidence: 99%

“…Several researchers [Kalli and Cashwell 1977;Rief et al 1984;Kulla and Fajardo 2012] have proposed importance sampling the geometry term between a vertex and positions on a ray. Kulla and Fajardo used this technique for rendering single scattering, and we generalize it to a vertex-segment connection technique in bidirectional sampling ( Figure 2c).…”

Section: Path Probability Density For Existing Techniquesmentioning

confidence: 99%

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Joint importance sampling of low-order volumetric scattering

et al. 2013

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Central to all Monte Carlo-based rendering algorithms is the construction of light transport paths from the light sources to the eye. Existing rendering approaches sample path vertices incrementally when constructing these light transport paths. The resulting probability density is thus a product of the conditional densities of each local sampling step, constructed without explicit control over the form of the final joint distribution of the complete path. We analyze why current incremental construction schemes often lead to high variance in the presence of participating media, and reveal that such approaches are an unnecessary legacy inherited from traditional surface-based rendering algorithms. We devise joint importance sampling of path vertices in participating media to construct paths that explicitly account for the product of all scattering and geometry terms along a sequence of vertices instead of just locally at a single vertex. This leads to a number of practical importance sampling routines to explicitly construct single-and double-scattering subpaths in anisotropically-scattering media. We demonstrate the benefit of our new sampling techniques, integrating them into several path-based rendering algorithms such as path tracing, bidirectional path tracing, and many-light methods. We also use our sampling routines to generalize deterministic shadow connections to connection subpaths consisting of two or three random decisions, to efficiently simulate higher-order multiple scattering. Our algorithms significantly reduce noise and increase performance in renderings with both isotropic and highly anisotropic, low-order scattering.

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“…Note that this PDF is exactly equal to that of equiangular sampling [Kalli and Cashwell 1977;Rief et al 1984;Kulla and Fajardo 2012] provided a, ω cb , and c are given.…”

Section: Unidirectional Factorization Pdfsmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Path Probability Density For Existing Techniquesmentioning

confidence: 99%

See 2 more Smart Citations

Joint importance sampling of low-order volumetric scattering

et al. 2013

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show abstract

“…(2) An infinite variance is possible when a collision occurs near the point due to the 1/R2 term in the analytical flux expression. In the past, numerous approaches (References [19][20][21][22] to eliminate or minimize these shortcomings have been tried. The approach of this work continues in this vein and produces a simple but accurate detector scheme which is efficient.…”

Section: P Point Estimation Technique For Rcpo1 P1 Introductionmentioning

confidence: 99%