Simulating the light transport of volumetric effects poses significant challenges and costs, especially in the presence of heterogeneous volumes. Generating stochastic paths for volume rendering involves multiple decisions, and previous works mainly focused on directional and distance sampling, where the volume scattering probability (VSP), i.e., the probability of scattering inside a volume, is indirectly determined as a byproduct of distance sampling. We demonstrate that direct control over the VSP can significantly improve efficiency and present an unbiased volume rendering algorithm based on an existing resampling framework for precise control over the VSP. Compared to previous state-of-the-art, which can only increase the VSP without guaranteeing to reach the desired value, our method also supports decreasing the VSP. We further present a data-driven guiding framework to efficiently learn and query an approximation of the optimal VSP everywhere in the scene without the need for user control. Our approach can easily be combined with existing path-guiding methods for directional sampling at minimal overhead and shows significant improvements over the state-of-the-art in various complex volumetric lighting scenarios.

Abstract We present a novel technique to efficiently render complex direct illumination in real‐time. It is based on a spatio‐temporal randomized mixture model of von Mises‐Fisher (vMF) distributions in screen space. For every pixel we determine the vMF distribution to sample from using a Markov chain process which is targeted to capture important features of the integrand. By this we avoid the storage overhead of finite‐component deterministic mixture models, for which, in addition, determining the optimal component count is challenging. We use stochastic multiple importance sampling (SMIS) to be independent of the equilibrium distribution of our Markov chain process, since it cancels out in the estimator. Further, we use the same sample to advance the Markov chain and to construct the SMIS estimator and local Markov chain state permutations avoid the resulting bias due to dependent sampling. As a consequence we require one ray per sample and pixel only. We evaluate our technique using implementations in a research renderer as well as a classic game engine with highly dynamic content. Our results show that it is efficient and quickly readapts to dynamic conditions. We compare to spatio‐temporal resampling (ReSTIR), which can suffer from correlation artifacts due to its non‐adapting candidate distributions that can deviate strongly from the integrand. While we focus on direct illumination, our approach is more widely applicable and we exemplarily show the rendering of caustics.

Russian roulette and splitting are widely used techniques to increase the efficiency of Monte Carlo estimators. But, despite their popularity, there is little work on how to best apply them. Most existing approaches rely on simple heuristics based on, e.g., surface albedo and roughness. Their efficiency often hinges on user-controlled parameters. We instead iteratively learn optimal Russian roulette and splitting factors during rendering, using a simple and lightweight data structure. Given perfect estimates of variance and cost, our fixed-point iteration provably converges to the optimal Russian roulette and splitting factors that maximize the rendering efficiency. In our application to unidirectional path tracing, we achieve consistent and significant speed-ups over the state of the art.

Path guiding is a promising tool to improve the performance of path tracing algorithms. However, not much research has investigated what target densities a guiding method should strive to learn for optimal performance. Instead, most previous work pursues the zero-variance goal: The local decisions are guided under the assumption that all other decisions along the random walk will be sampled perfectly. In practice, however, many decisions are poorly guided, or not guided at all. Furthermore, learned distributions are often marginalized, e.g., by neglecting the BSDF. We present a generic procedure to derive theoretically optimal target densities for local path guiding. These densities account for variance in nested estimators, and marginalize provably well over, e.g., the BSDF. We apply our theory in two state-of-the-art rendering applications: a path guiding solution for unidirectional path tracing [Müller et al. 2017] and a guiding method for light source selection for the many lights problem [Vévoda et al. 2018]. In both cases, we observe significant improvements, especially on glossy surfaces. The implementations for both applications consist of trivial modifications to the original code base, without introducing any additional overhead.

Effective local light transport guiding demands for high quality guiding information, i.e., a precise representation of the directional incident radiance distribution at every point inside the scene. We introduce a parallax-aware distribution model based on parametric mixtures. By parallax-aware warping of the distribution, the local approximation of the 5D radiance field remains valid and precise across large spatial regions, even for close-by contributors. Our robust optimization scheme fits parametric mixtures to radiance samples collected in previous rendering passes. Robustness is achieved by splitting and merging of components refining the mixture. These splitting and merging decisions minimize and bound the expected variance of the local radiance estimator. In addition, we extend the fitting scheme to a robust, iterative update method, which allows for incremental training of our model using smaller sample batches. This results in more frequent training updates and, at the same time, significantly reduces the required sample memory footprint. The parametric representation of our model allows for the application of advanced importance sampling methods such as radiance-based, cosine-aware, and even product importance sampling. Our method further smoothly integrates next-event estimation (NEE) into path guiding, avoiding importance sampling of contributions better covered by NEE. The proposed robust fitting and update scheme, in combination with the parallax-aware representation, results in faster learning and lower variance compared to state-of-the-art path guiding approaches.

Abstract Physically based rendering is a well‐understood technique to produce realistic‐looking images. However, different algorithms exist for efficiency reasons, which work well in certain cases but fail or produce rendering artefacts in others. Few tools allow a user to gain insight into the algorithmic processes. In this work, we present such a tool, which combines techniques from information visualization and visual analytics with physically based rendering. It consists of an interactive parallel coordinates plot, with a built‐in sampling‐based data reduction technique to visualize the attributes associated with each light sample. Two‐dimensional (2D) and three‐dimensional (3D) heat maps depict any desired property of the rendering process. An interactively rendered 3D view of the scene displays animated light paths based on the user's selection to gain further insight into the rendering process. The provided interactivity enables the user to guide the rendering process for more efficiency. To show its usefulness, we present several applications based on our tool. This includes differential light transport visualization to optimize light setup in a scene, finding the causes of and resolving rendering artefacts, such as fireflies, as well as a path length contribution histogram to evaluate the efficiency of different Monte Carlo estimators.

The efficiency of Monte Carlo methods, commonly used to render participating media, is directly linked to the manner in which random sampling decisions are made during path construction. Notably, path construction is influenced by scattering direction and distance sampling, Russian roulette, and splitting strategies. We present a consistent suite of volumetric path construction techniques where all these sampling decisions are guided by a cached estimate of the adjoint transport solution . The proposed strategy is based on the theory of zero-variance path sampling schemes, accounting for the spatial and directional variation in volumetric transport. Our key technical contribution, enabling the use of this approach in the context of volume light transport, is a novel guiding strategy for sampling the particle collision distance proportionally to the product of transmittance and the adjoint transport solution (e.g., in-scattered radiance). Furthermore, scattering directions are likewise sampled according to the product of the phase function and the incident radiance estimate. Combined with guided Russian roulette and splitting strategies tailored to volumes, we demonstrate about an order-of-magnitude error reduction compared to standard unidirectional methods. Consequently, our approach can render scenes otherwise intractable for such methods, while still retaining their simplicity (compared to, e.g., bidirectional methods).

The efficiency of Monte Carlo algorithms for light transport simulation is directly related to their ability to importance-sample the product of the illumination and reflectance in the rendering equation. Since the optimal sampling strategy would require knowledge about the transport solution itself, importance sampling most often follows only one of the known factors – BRDF or an approximation of the incident illumination. To address this issue, we propose to represent the illumination and the reflectance factors by the Gaussian mixture model (GMM), which we fit by using a combination of weighted expectation maximization and non-linear optimization methods. The GMM representation then allows us to obtain the resulting product distribution for importance sampling on-the-fly at each scene point. For its efficient evaluation and sampling we preform an up-front adaptive decimation of both factor mixtures. In comparison to state-of-the-art sampling methods, we show that our product importance sampling can lead to significantly better convergence in scenes with complex illumination and reflectance.