We present two novel unbiased techniques for sampling free paths in heterogeneous participating media. Our decomposition tracking accelerates free-path construction by splitting the medium into a control component and a residual component and sampling each of them separately. To minimize expensive evaluations of spatially varying collision coefficients, we define the control component to allow constructing free paths in closed form. The residual heterogeneous component is then homogenized by adding a fictitious medium and handled using weighted delta tracking, which removes the need for computing strict bounds of the extinction function. Our second contribution, spectral tracking, enables efficient light transport simulation in chromatic media. We modify free-path distributions to minimize the fluctuation of path throughputs and thereby reduce the estimation variance. To demonstrate the correctness of our algorithms, we derive them directly from the radiative transfer equation by extending the integral formulation of null-collision algorithms recently developed in reactor physics. This mathematical framework, which we thoroughly review, encompasses existing trackers and postulates an entire family of new estimators for solving transport problems; our algorithms are examples of such. We analyze the proposed methods in canonical settings and on production scenes, and compare to the current state of the art in simulating light transport in heterogeneous participating media.

Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novák. Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2017). 36(4), Article 111, July 2017.

@article{Kutz2017SDT,
    author = {Kutz., Peter and Habel, Ralf and Li, Yining Karl and Nov\'{a}k, Jan},
    title = {Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes},
    journal = {ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2017)},
    volume = {36},
    number = {4},
    month = jul,
    year = {2017},
    articleno = {111},
    doi = {10.1145/3072959.3073665},
    keywords = {participating media, volume rendering, free-path sampling, transmittance, delta tracking, ratio tracking, color},
}

We thank Patrick Kelly for implementing various components of our volume rendering system, as well as for numerous discussions, and David Adler for help with profiling the code. Alex Nijmeh and Henrik Falt created the cloud scenes used in Figure 1 and Figure 11. Jesse Erickson created the colored explosion in Figure 12. The geometry of the dragon in Figure 15 is from the Stanford Computer Graphics Laboratory. We thank Thomas Müller, Marios Papas, Géraldine Conti, and David Adler for proofreading, and Brent Burley, Michael Kaschalk, and Rajesh Sharma for providing support, encouragement, and resources for this project. All images were rendered using Disney’s Hyperion Renderer.

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