Residual Ratio Tracking for Estimating Attenuation in Participating Media

1Walt Disney Animation Studios 2Disney Research Zürich

In ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 2014

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.


Evaluating 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.


Text Reference

Jan Novák, Andrew Selle, Wojciech Jarosz. Residual Ratio Tracking for Estimating Attenuation in Participating Media. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 33(6), November 2014.

BibTex Reference

    author = "Novák, Jan and Selle, Andrew and Jarosz, Wojciech",
    title = "Residual Ratio Tracking for Estimating Attenuation in Participating Media",
    journal = "ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)",
    volume = "33",
    number = "6",
    year = "2014",
    month = "nov",
    keywords = "transmittance, fractional visibility, opacity, ray marching, woodcock tracking, delta tracking, pseudo-scattering, null-collision",
    doi = "10.1145/2661229.2661292"

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