Unbiased Light Transport Estimators for Inhomogeneous Participating Media

Abstract

Figure 1: Transmittance (left), single-scatter of a point light source (middle), and multiple-scatter (right) calculation for 12-octave Perlinnoise medium and comparison to Woodcock tracking with equal number of medium fetches. AbstractThis 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.

Multiple Scattering in Inhomogeneous Participating Media Using Rao‐Blackwellization and Control Variates

“…The ratio tracking method [NSJ14] modified the weights of light particles instead of randomly terminating them, and the residual ratio tracking method combined the weighting scheme with control variates. This concept has been further generalized giving physical interpretation of non‐majorant sampling and even for negative extinction [SKGM* 17] showing up when the control variate is not a minorant. In these methods control variates were used to compute the transmittance between two given points and not during free flight.…”

“…The method of this paper exploits the data generated during a pre‐processing step similarly to [SKTM11, KHLN17], works with non‐bounding majorant in sampling and approximate minorant in decomposition as [SKGM* 17, KHLN17], and naturally extends to spectral tracking. According to our knowledge, this is the first paper that exploits the statistical method of control variates for the extinction in multiple scattering rendering and non‐trivially combines the control variates of the extinction and the scattered radiance.…”

“…where w = ∑ m δ 2 m /μ m is the only parameter that depends on the sampling strategy and is called the variance introduction density [SKGM*17]. The expectation of the transmitted weight is the same as in Eq.…”

“…Sections 3 and 4 discuss our new model and rendering algorithm. Finally, Section 5 presents rendering results and we compare the new method to Woodcock tracking [WMHL65], generalized residual ratio tracking [NSJ14, SKGM*17] and weighted decomposition tracking [KHLN17].…”

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

“…Thus, the efficient physical simulation of particle transfer in heterogeneous media is essential. We have developed a behaviorally valid model that works differently than the real particles, but provides the same expectations and its relevant parts can analytically be evaluated [114]. In volume visualization and tomographic reconstruction, box splines are mainly used as reconstruction kernels.…”