Residual ratio tracking for estimating attenuation in participating media

Abstract

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.

A Path‐Tracing Monte Carlo Library for 3‐D Radiative Transfer in Highly Resolved Cloudy Atmospheres

“…However, while they use NCAs in acceleration grids, they do not achieve insensitivity of computing times to the resolution of the volumetric data. With distinct applicative objectives, strong efforts have also been made by the film industry, especially by Disney Research, which revisited NCAs and transformed them into a validated industrial practice (Kutz et al, ; Novák et al, , ).…”

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

“…It was shown [SKTM11] that Woodcock tracking and control variates can also be exploited for transmittance calculation, which requires a minorant of the extinction. 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.…”

“…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].…”

Real-time online learning of Gaussian mixture model for opacity mapping

“…In the presence of heterogeneous participating media, the light transport is governed by the radiative transport equation (RTE). When solving this equation for multiple scattering, even the recent stochastic sampling technique based on Poisson process simulation is far from real-time [2]. The opacity mapping is an extension of the shadow mapping as the image-based transparency [3] for direct volumetric lighting.…”