Unbiased Light Transport Estimators for Inhomogeneous Participating Media

László Szirmay-Kalos, Iliyan Georgiev, Milán Magdics, Balázs Molnár, and Dávid Légrády
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Magyar tudósok krt. 2, H-1117, HUNGARY;

Solid Angle, email: iliyan@solidangle.com



This paper presents a new stochastic particle model for efficient and unbiased Monte Carlo rendering of heterogeneous participating media.We randomly add and remove material particles to obtain a density with which free flight sampling and transmittance estimation are simple, while material particle properties are simultaneously modified to maintain the true expectation of the radiance. We show that meeting this requirement may need the introduction of light particles with negative energy and materials with negative extinction, and provide an intuitive interpretation for such phenomena. Unlike previous unbiased methods, the proposed approach does not require a-priori knowledge of the maximum medium density that is typically difficult to obtain for procedural models. However, the method can benefit from an approximate knowledge of the density, which can usually be acquired on-the-fly at little extra cost and can greatly reduce the variance of the proposed estimators. The introduced mechanism can be integrated in participating media renderers where transmittance estimation and free flight sampling are building blocks. We demonstrate its application in a multiple scattering particle tracer, in transmittance computation, and in the estimation of the inhomogeneous air-light integral.


Participating media, transmittance, free path sampling, Woodcock tracking, Monte Carlo method, Volumetric global illumination, procedural models, Perlin noise.