Free Path Sampling in High Resolution Inhomogeneous Participating Media

Szirmay‐Kalos, László; Tóth, Bence; Magdics, Milán

doi:10.1111/j.1467-8659.2010.01831.x

Cited by 51 publications

(45 citation statements)

References 18 publications

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“…constant control extinction in our case) can reduce variance if it decreases the rate of change of the residual exponentiated integral. The residual tracking is also related to the "separation of main part" applied by Szirmay-Kalos et al [2011] to the evaluation of optical thickness. However, their approach will be effective only if the main part is represented by a non-constant function that matches the extinction function well.…”

Section: Residual Trackingmentioning

confidence: 99%

“…Unbiased free-flight sampling routines can also be used for estimating transmittance [Raab et al 2008;Szirmay-Kalos et al 2011;Jarosz et al 2011]: if the sampled free flight distance is greater than d, the transmittance is estimated as 1, and 0 otherwise. The binary estimate can be further refined by averaging multiple instances, i.e.…”

Section: Free-flight Sampling As a Transmittance Estimatementioning

confidence: 99%

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Residual ratio tracking for estimating attenuation in participating media

2014

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Figure 1: A cloudy sky rendered with our residual ratio tracking estimator for computing transmittance in heterogeneous volumes. Our technique is unbiased, outperforms the delta tracking-based estimator (b), and fits well into path-tracing, production frameworks. The insets show renderings of absorptive-only (top) and scattering (bottom) clouds; the transmittance was estimated using delta tracking (b), ratio tracking (c), and residual ratio tracking (d) with a roughly equal cost reported as the number of extinction coefficient evaluations. Images ©Disney. AbstractEvaluating transmittance within participating media is a fundamental operation required by many light transport algorithms. We present ratio tracking and residual tracking, two complementary techniques that can be combined into an efficient, unbiased estimator for evaluating transmittance in complex heterogeneous media. In comparison to current approaches, our new estimator is unbiased, yields high efficiency, gracefully handles media with wavelength dependent extinction, and bridges the gap between closed form solutions and purely numerical, unbiased approaches. A key feature of ratio tracking is its ability to handle negative densities. This in turn enables us to separate the main part of the transmittance function, handle it analytically, and numerically estimate only the residual transmittance. In addition to proving the unbiasedness of our estimators, we perform an extensive empirical analysis to reveal parameters that lead to high efficiency. Finally, we describe how to integrate the new techniques into a production path tracer and demonstrate their benefits over traditional unbiased estimators.

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Section: Residual Trackingmentioning

confidence: 99%

Section: Free-flight Sampling As a Transmittance Estimatementioning

confidence: 99%

Residual ratio tracking for estimating attenuation in participating media

2014

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“…To improve efficiency, the original medium is usually approximated by functions allowing analytical integration and sampling. Note that recently, sampling of arbitrary media has received a lot of attention [14,15]. An accurate and multi-resolution representation is the octree.…”

Section: Discussionmentioning

confidence: 99%

Globally Adaptive Control Variate for Robust Numerical Integration

Pajot¹,

Barthe²,

Paulin³

2014

SIAM J. Sci. Comput.

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Abstract. Many methods in computer graphics require the integration of functions on lowto-middle-dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration method, able to handle arbitrary non-singular scalar or vector-valued functions defined on low-to-middle-dimensional spaces. Our method combines control variate, globally adaptive subdivision and Monte-Carlo estimation to achieve fast and accurate computations of any non-singular integral. The runtime is linear with respect to standard deviation while standard Monte-Carlo methods are quadratic. We additionally show through numerical tests that our method is extremely stable from a computation time and memory footprint point-of-view, assessing its robustness. We demonstrate our method on a participating media voxelization application, which requires the computation of several millions integrals for complex media.

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“…Woodcock tracking is a technique developed in the particle physics field for unbiased mean-free path sampling. Several recent graphics techniques [Raab et al 2008;Szirmay-Kalos et al 2011] have employed this, in combination with Equation (20), for estimating transmittance in heterogeneous media.…”

Section: Evaluating γ In Heterogeneous Mediamentioning

confidence: 98%

“…We found that performance loss of each pass is primarily due to multiple evaluations of Perlin noise, which is quite expensive both on the GPU and CPU. Accelerated variants of Woodcock tracking [Yue et al 2010;Szirmay-Kalos et al 2011] could help to reduce the number of density evaluations needed for free-path sampling.…”

Section: Limitations and Future Workmentioning

confidence: 99%

Progressive photon beams

Jarosz

Nowrouzezahrai

Thomas

et al. 2011

Proceedings of the 2011 SIGGRAPH Asia Conference

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Average Pass Final Image Heterogeneous 16.8 minutes 15.04 M beams Homogeneous 9.5 minutes 14.55 M beams Homogeneous 3.0 minutes 19.67 M beams Homogeneous 8.0 minutes 2.09 M beams Heterogeneous 5.7 minutes 16.19 M beams Heterogeneous 10.8 minutes 2.09 M beams Heterogeneous 16.8 minutes 15.04 M beams Homogeneous 9.5 minutes 14.55 M beams Homogeneous 3.0 minutes 19.67 M beams Homogeneous 8.0 minutes 2.09 M beams Heterogeneous 5.7 minutes 16.19 M beams Heterogeneous 10.8 minutes 2.09 M beams Figure 1: The CARS, DISCO, and FLASHLIGHTS scenes rendered using progressive photon beams for both homogeneous and heterogeneous media. We generate a sequence of independent render passes (middle) where we progressively reduce the photon beam radii. This slightly increases variance in each pass, but we prove that the average of all passes (bottom) converges to the ground truth. AbstractWe present progressive photon beams, a new algorithm for rendering complex lighting in participating media. Our technique is efficient, robust to complex light paths, and handles heterogeneous media and anisotropic scattering while provably converging to the correct solution using a bounded memory footprint. We achieve this by extending the recent photon beams variant of volumetric photon mapping. We show how to formulate a progressive radiance estimate using photon beams, providing the convergence guarantees and bounded memory usage of progressive photon mapping. Progressive photon beams can robustly handle situations that are difficult for most other algorithms, such as scenes containing participating media and specular interfaces, with realistic light sources completely enclosed by refractive and reflective materials. Our technique handles heterogeneous media and also trivially supports stochastic effects such as depth-of-field and glossy materials. Finally, we show how progressive photon beams can be implemented efficiently on the GPU as a splatting operation, making it applicable to interactive and real-time applications. These features make our technique scalable, providing the same physically-based algorithm for interactive feedback and reference-quality, unbiased solutions.

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Free Path Sampling in High Resolution Inhomogeneous Participating Media

Cited by 51 publications

References 18 publications

Residual ratio tracking for estimating attenuation in participating media

Residual ratio tracking for estimating attenuation in participating media

Globally Adaptive Control Variate for Robust Numerical Integration

Progressive photon beams

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