5D Covariance tracing for efficient defocus and motion blur

Belcour, Laurent; Soler, Cyril; Subr, Kartic; Holzschuch, Nicolas; Durand, Frédo

doi:10.1145/2487228.2487239

Cited by 63 publications

(67 citation statements)

References 60 publications

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“…Further work led to efficient algorithms for sampling the lens aperture [Soler et al 2009] as well as time [Egan et al 2009] domains. Belcour et al [2012] present an algorithm to propagate approximate spectral information of the 5D local light field. These approaches together provide approximate information about the Fourier spectrum of the integrand.…”

Section: Related Workmentioning

confidence: 99%

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Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration

Subr

Kautz

2013

ACM Trans. Graph.

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Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these highdimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image.We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.

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Section: Related Workmentioning

confidence: 99%

“…For integration of bandlimited signals, spectral aliases introduce error in the estimates when the sampling is below half this rate [Křivánek and Colbert 2008;Durand 2011;Belcour et al 2012]. Figure 1 illustrates the difference between errors in reconstruction and integration.…”

Section: Related Workmentioning

confidence: 99%

Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration

Subr

Kautz

2013

ACM Trans. Graph.

Self Cite

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“…Furthermore, it would be desirable to have multiple spectral targets embedded in our hierarchical tile-based sampling system. The ideas presented in [Belcour et al 2013] may be pertinent to this extension.…”

Section: Resultsmentioning

confidence: 99%

Fast tile-based adaptive sampling with user-specified Fourier spectra

et al. 2014

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We introduce a fast tile-based method for adaptive two-dimensional sampling with user-specified spectral properties. At the core of our approach is a deterministic, hierarchical construction of self-similar, equi-area, tri-hex tiles whose centroids have a spatial distribution free of spurious spectral peaks. A lookup table of sample points, computed offline using any existing point set optimizer to shape the samples' Fourier spectrum, is then used to populate the tiles. The result is a linear-time, adaptive, and high-quality sampling of arbitrary density functions that conforms to the desired spectral distribution, achieving a speed improvement of several orders of magnitude over current spectrum-controlled sampling methods.

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“…Light transport analysis formulates these transformations and exploits the structure of the transformed light field for various applications, including synthetic image or light field rendering [Chai et al 2000;Durand et al 2005;Egan et al 2009;Egan et al 2011;Lehtinen et al 2011;Jarosz et al 2012;Belcour et al 2012], processing for light field cameras and displays [Ng 2005;Zwicker et al 2006;Levin and Durand 2010;Wetzstein et al 2012], image formation modeling [Levin et al 2009;Liang et al 2011], and inverse transport analysis [Ramamoorthi and Hanrahan 2001;Seitz et al 2005]. Our approach leverages these foundational analyses, and focuses on analyzing the resolution of lenslet-based light field cameras.…”

Section: Related Workmentioning

confidence: 99%

A Light Transport Framework for Lenslet Light Field Cameras

Liang¹,

Ramamoorthi

2015

ACM Trans. Graph.

100

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Light field cameras capture full spatio-angular information of the light field, and enable many novel photographic and scientific applications. It is often stated that there is a fundamental tradeoff between spatial and angular resolution, but there has been limited understanding of this tradeoff theoretically or numerically. Moreover, it is very difficult to evaluate the design of a light field camera, because a new design is usually reported with its prototype and rendering algorithm, all of which affect resolution.In this paper, we develop a light transport framework for understanding the fundamental limits of light field camera resolution. We first derive the prefiltering model of lenslet-based light field cameras. The main novelty of our model is in considering the full space-angle sensitivity profile of the photosensor-in particular, real pixels have non-uniform angular sensitivity, responding more to light along the optical axis, rather than at grazing angles. We show that the full sensor profile plays an important role in defining the performance of a light field camera. The proposed method can model all existing lenslet-based light field cameras and allows us to compare them in a unified way in simulation, independent of the practical differences between particular prototypes. We further extend our framework to analyze the performance of two rendering methods: the simple projection-based method and the inverse light transport process. We validate our framework with both flatland simulation and real data from the Lytro light field camera.

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5D Covariance tracing for efficient defocus and motion blur

Cited by 63 publications

References 60 publications

Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration

Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration

Fast tile-based adaptive sampling with user-specified Fourier spectra

A Light Transport Framework for Lenslet Light Field Cameras

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