Figure 1: A comparison of our vertex connection and merging (VCM) algorithm against bidirectional path tracing (BPT) and stochastic progressive photon mapping (PPM).Overview. Light transport simulation is an essential element in realistic image synthesis for computer-generated imagery. However, developing robust light transport simulation algorithms that are capable of dealing with arbitrary input scenes (scene geometry, surface reflectance, light sources) remains an elusive challenge. Although efficient light transport algorithms exist, an acceptable approximation error in a reasonable amount of time is usually only achieved for specific types of inputs. To address this problem, we present [1] a reformulation of the popular density estimator, known in computer graphics as "photon mapping" [2-4], as a bidirectional path sampling technique for Monte Carlo light transport simulation [6]. The benefit of our new formulation is twofold. First, it makes it possible to explain the relative efficiency of photon mapping and bidirectional path tracing [5,7,8] algorithms, which have so far been considered conceptually incompatible solutions. Perhaps more importantly, it allows for a seamless integration of the two methods into a more robust combined light transport simulation algorithm, dubbed vertex connection and merging, or VCM. A progressive version of this algorithm is consistent and efficiently handles a wide variety of lighting conditions, ranging from direct illumination and diffuse inter-reflections to specular-diffuse-specular light transport, which is notoriously difficult for bidirectional path tracing. Our theoretical analysis shows that VCM inherits the high asymptotic performance from bidirectional path tracing for most light transport path types, while benefiting from the efficiency of photon mapping for specular-diffuse-specular lighting effects.Results. A comparison of our vertex connection and merging (VCM) algorithm against bidirectional path tracing (BPT) and progressive photon mapping (PPM) [2,4] after 30 min of rendering is shown in Figure 1. BPT fails to reproduce the light focused by the vase and reflected in the mirror (specular-diffuse-specular transport paths), while PPM has difficulties handling the illumination coming from the room seen in the mirror. Our VCM algorithm automatically computes a good mixture of sampling techniques from BPT and PPM to robustly capture the entire illumination. The rightmost column shows, in false color, the relative contributions of the path sampling techniques from BPT and PPM, respectively, to the VCM image.

The wide adoption of path‐tracing algorithms in high‐end realistic rendering has stimulated many diverse research initiatives. In this paper we present a coherent survey of methods that utilize Monte Carlo integration for estimating light transport in scenes containing participating media. Our work complements the volume‐rendering state‐of‐the‐art report by Cerezo et al. [CPP*05]; we review publications accumulated since its publication over a decade ago, and include earlier methods that are key for building light transport paths in a stochastic manner. We begin by describing analog and non‐analog procedures for free‐path sampling and discuss various expected‐value, collision, and track‐length estimators for computing transmittance. We then review the various rendering algorithms that employ these as building blocks for path sampling. Special attention is devoted to null‐collision methods that utilize fictitious matter to handle spatially varying densities; we import two “next‐flight” estimators originally developed in nuclear sciences. Whenever possible, we draw connections between image‐synthesis techniques and methods from particle physics and neutron transport to provide the reader with a broader context.

Scattering from specular surfaces produces complex optical effects that are frequently encountered in realistic scenes: intricate caustics due to focused reflection, multiple refraction, and high-frequency glints from specular microstructure. Yet, despite their importance and considerable research to this end, sampling of light paths that cause these effects remains a formidable challenge. In this article, we propose a surprisingly simple and general sampling strategy for specular light paths including the above examples, unifying the previously disjoint areas of caustic and glint rendering into a single framework. Given two path vertices, our algorithm stochastically finds a specular subpath connecting the endpoints. In contrast to prior work, our method supports high-frequency normal- or displacement-mapped geometry, samples specular-diffuse-specular ("SDS") paths, and is compatible with standard Monte Carlo methods including unidirectional path tracing. Both unbiased and biased variants of our approach can be constructed, the latter often significantly reducing variance, which may be appealing in applied settings (e.g. visual effects). We demonstrate our method on a range of challenging scenes and evaluate it against state-of-the-art methods for rendering caustics and glints.

Efficiently computing light transport in participating media in a manner that is robust to variations in media density, scattering albedo, and anisotropy is a difficult and important problem in realistic image synthesis. While many specialized rendering techniques can efficiently resolve subsets of transport in specific media, no single approach can robustly handle all types of effects. To address this problem we unify volumetric density estimation, using point and beam estimators, and Monte Carlo solutions to the path integral formulation of the rendering and radiative transport equations. We extend multiple importance sampling to correctly handle combinations of these fundamentally different classes of estimators. This, in turn, allows us to develop a single rendering algorithm that correctly combines the benefits and mediates the limitations of these powerful volume rendering techniques.

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