Spectrally optimal sampling for distribution ray tracing

Mitchell, Don P.

doi:10.1145/122718.122736

Cited by 116 publications

(89 citation statements)

References 10 publications

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“…Ulichney [1987] was the first to provide qualitative characterization of a good sampling pattern, which is now commonly called Blue Noise. Mitchell [1991] has also pointed out that energy in low-frequency part of the Fourier spectrum of the sampling pattern should be avoided. Since then, different algorithms [Balzer et al 2009;Schlömer et al 2011;de Goes et al 2012] and tile-based Spherical harmonic function of degree l and order m whose inner product over the sphere is 4π P m l (cos θ) associated Legendre polynomial of degree l and order m. Θ the Fourier domain without the DC peak.…”

Section: Related Work Sampling In Euclidean Domainmentioning

confidence: 99%

Variance analysis for Monte Carlo integration

et al. 2015

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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. We build our framework in the Euclidean space using Fourier tools and on the sphere using spherical harmonics. We further provide a theoretical background that explains how our spherical framework can be extended to the hemispherical domain. 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. Furthermore, we formulate design principles for constructing sampling methods that can be tailored according to available resources. We validate our theoretical framework by performing numerical integration over several integrands sampled using different sampling patterns.

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Section: Related Work Sampling In Euclidean Domainmentioning

confidence: 99%

Variance analysis for Monte Carlo integration

et al. 2015

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“…Stratification helps to reduce the variance compared to uniformly random sampling patterns [19]. Discussions of the relationship between the dimensionality of the sample space and the variance in computer graphics problems V x y dxdy V x f x dx ( , ) ( , ( )) r r r r r r r ∫ ∫ ∫ ≈ can be found in [18,19]. A variance measurement experiment involving fourdimensional double-area integration can be found in [18].…”

Section: Discussion Of Deterministic Ray Tracingmentioning

confidence: 99%

“…Discussions of the relationship between the dimensionality of the sample space and the variance in computer graphics problems V x y dxdy V x f x dx ( , ) ( , ( )) r r r r r r r ∫ ∫ ∫ ≈ can be found in [18,19]. A variance measurement experiment involving fourdimensional double-area integration can be found in [18]. A comparison between tracing one random ray at each pixel sample versus tracing one correlated ray at each pixel sample is given in the color plate.…”

Section: Discussion Of Deterministic Ray Tracingmentioning

confidence: 99%

Shadow Penumbras for Complex Objects by Depth-Dependent Filtering of Multi-Layer Depth Images

Keating

Max

1999

Eurographics

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January 12, 1999This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author. Abstract. This paper presents an efficient algorithm for filtering multi-layer depth images (MDIs) in order to produce approximate penumbras. The filtering is performed on a MDI that represents the view from the light source. The algorithm is based upon both ray tracing and the z-buffer shadow algorithm, and is closely related to convolution methods. The method's effectiveness is demonstrated on especially complex objects such as trees, whose soft shadows are expensive to compute by other methods. The method specifically addresses the problem of light-leaking that occurs when tracing rays through discrete representations, and the inability of convolution methods to produce accurate self-shadowing effects. PREPRINT

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“…Our goal to use fewer samples where the integrand is smoother follows a long line of adaptive sampling methods, e.g. [Whitted 1980;Mitchell 1987;1991;Kirk and Arvo 1991]. Multidimensional adaptive sampling [Hachisuka et al 2008] adapts sampling in the full 5D domain, according to variance estimated from the samples themselves.…”

Section: Sparse and Low-rank Approximations Of Light Transportmentioning

confidence: 99%

5D Covariance tracing for efficient defocus and motion blur

et al. 2013

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The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We dramatically accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the covariance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects.

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Spectrally optimal sampling for distribution ray tracing

Cited by 116 publications

References 10 publications

Variance analysis for Monte Carlo integration

Variance analysis for Monte Carlo integration

Shadow Penumbras for Complex Objects by Depth-Dependent Filtering of Multi-Layer Depth Images

5D Covariance tracing for efficient defocus and motion blur

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