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Temporal Sample Reuse for Next Event Estimation and Path Guiding for Real-Time Path Tracing
(The Eurographics Association, 2020) Dittebrandt, Addis; Hanika, Johannes; Dachsbacher, Carsten; Dachsbacher, Carsten and Pharr, Matt
Good importance sampling is crucial for real-time path tracing where only low sample budgets are possible. We present two efficient sampling techniques tailored for massively-parallel GPU path tracing which improve next event estimation (NEE) for rendering with many light sources and sampling of indirect illumination. As sampling densities need to vary spatially, we use an octree structure in world space and introduce algorithms to continuously adapt the partitioning and distribution of the sampling budget. Both sampling techniques exploit temporal coherence by reusing samples from the previous frame: For NEE we collect sampled, unoccluded light sources and show how to deduplicate, but also diffuse this information to efficiently sample light sources in the subsequent frame. For sampling indirect illumination, we present a compressed directional quadtree structure which is iteratively adapted towards high-energy directions using samples from the previous frame. The updates and rebuilding of all data structures takes about 1ms in our test scenes, and adds about 6ms at 1080p to the path tracing time compared to using state-of-the-art light hierarchies and BRDF sampling. We show that this additional effort reduces noise in terms of mean squared error by at least one order of magnitude in many situations.
A Study of Observer Metamerism for Reflectance-induced Stimuli
(The Eurographics Association, 2024) Fascione, Luca; Hanika, Johannes; Hardeberg, Jon Yngve; Rushmeier, Holly
Cameras make images collecting per-pixel measurements of light reflected by the objects in the world. Commonly, these measurements undergo a transformation so that they become values in a standardized color space, such as the sRGB space. This makes it possible to send the values to a display device and produce in a human a visual sensation as close as possible to what would have been caused by the original scene. In this work we aim to explore the difficulties and opportunities that arise in devising such non-bijective transformations, visualizing differences between device vision and human vision. In particular we are interested in the practical impact of observer metamerism: different camera devices and human observers can distinguish a different set of spectral stimuli presented to them. When characterizing a camera, this is usually ignored, missing potential to increase chromatic acuity where the camera can see more than the human observer. A question that arises is whether the metameric stimuli involved here do actually appear in practice in relevant cases. We run numeric experiments to investigate these questions.
Path Guiding with Vertex Triplet Distributions
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Schüßler, Vincent; Hanika, Johannes; Jung, Alisa; Dachsbacher, Carsten; Ghosh, Abhijeet; Wei, Li-Yi
Good importance sampling strategies are decisive for the quality and robustness of photorealistic image synthesis with Monte Carlo integration. Path guiding approaches use transport paths sampled by an existing base sampler to build and refine a guiding distribution. This distribution then guides subsequent paths in regions that are otherwise hard to sample. We observe that all terms in the measurement contribution function sampled during path construction depend on at most three consecutive path vertices. We thus propose to build a 9D guiding distribution over vertex triplets that adapts to the full measurement contribution with a 9D Gaussian mixture model (GMM). For incremental path sampling, we query the model for the last two vertices of a path prefix, resulting in a 3D conditional distribution with which we sample the next vertex along the path. To make this approach scalable, we partition the scene with an octree and learn a local GMM for each leaf separately. In a learning phase, we sample paths using the current guiding distribution and collect triplets of path vertices. We resample these triplets online and keep only a fixed-size subset in reservoirs. After each progression, we obtain new GMMs from triplet samples by an initial hard clustering followed by expectation maximization. Since we model 3D vertex positions, our guiding distribution naturally extends to participating media. In addition, the symmetry in the GMM allows us to query it for paths constructed by a light tracer. Therefore our method can guide both a path tracer and light tracer from a jointly learned guiding distribution.
Bridge Sampling for Connections via Multiple Scattering Events
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Schüßler, Vincent; Hanika, Johannes; Dachsbacher, Carsten; Garces, Elena; Haines, Eric
Explicit sampling of and connecting to light sources is often essential for reducing variance in Monte Carlo rendering. In dense, forward-scattering participating media, its benefit declines, as significant transport happens over longer multiple-scattering paths around the straight connection to the light. Sampling these paths is challenging, as their contribution is shaped by the product of reciprocal squared distance terms and the phase functions. Previous work demonstrates that sampling several of these terms jointly is crucial. However, these methods are tied to low-order scattering or struggle with highly-peaked phase functions. We present a method for sampling a bridge: a subpath of arbitrary vertex count connecting two vertices. Its probability density is proportional to all phase functions at inner vertices and reciprocal squared distance terms. To achieve this, we importance sample the phase functions first, and subsequently all distances at once. For the latter, we sample an independent, preliminary distance for each edge of the bridge, and afterwards scale the bridge such that it matches the connection distance. The scale factor can be marginalized out analytically to obtain the probability density of the bridge. This approach leads to a simple algorithm and can construct bridges of any vertex count. For the case of one or two inserted vertices, we also show an alternative without scaling or marginalization. For practical path sampling, we present a method to sample the number of bridge vertices whose distribution depends on the connection distance, the phase function, and the collision coefficient. While our importance sampling treats media as homogeneous we demonstrate its effectiveness on heterogeneous media.
Portal-Based Path Perturbation for Metropolis Light Transport
(The Eurographics Association, 2020) Otsu, Hisanari; Hanika, Johannes; Dachsbacher, Carsten; Krüger, Jens and Niessner, Matthias and Stückler, Jörg
Light transport simulation in scenes with difficult visibility still remains a challenging problem. Markov chain Monte Carlo (MCMC) rendering is often employed for such configurations. It generates a sequence of correlated light transport paths by iteratively mutating the current state, a path, to another. Since the proposed path is correlated to the current path, MCMC can explore regions of the path space, also with difficult visibility, once they have been found. To improve the efficiency of the exploration, we propose a path mutation strategy making use of the concept of portals. Portals are user-defined objects in the scene to guide the sampling of the difficult visibility, which have been employed in the context of non-MCMC rendering. Our mutation strategy perturbs a path edge around the intersection point of the edge and the portal, instead of perturbing the edge by moving a path vertex as in the ordinary path mutation strategies. This reduces the probability for the proposed path being rejected due to changes in visibility.
Optimised Path Space Regularisation
(The Eurographics Association and John Wiley & Sons Ltd., 2021) Weier, Philippe; Droske, Marc; Hanika, Johannes; Weidlich, Andrea; Vorba, Jirí; Bousseau, Adrien and McGuire, Morgan
We present Optimised Path Space Regularisation (OPSR), a novel regularisation technique for forward path tracing algorithms. Our regularisation controls the amount of roughness added to materials depending on the type of sampled paths and trades a small error in the estimator for a drastic reduction of variance in difficult paths, including indirectly visible caustics. We formulate the problem as a joint bias-variance minimisation problem and use differentiable rendering to optimise our model. The learnt parameters generalise to a large variety of scenes irrespective of their geometric complexity. The regularisation added to the underlying light transport algorithm naturally allows us to handle the problem of near-specular and glossy path chains robustly. Our method consistently improves the convergence of path tracing estimators, including state-of-the-art path guiding techniques where it enables finding otherwise hard-to-sample paths and thus, in turn, can significantly speed up the learning of guiding distributions.
A Microfacet-based Hair Scattering Model
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Huang, Weizhen; Hullin, Matthias B.; Hanika, Johannes; Ghosh, Abhijeet; Wei, Li-Yi
The development of scattering models and rendering algorithms for human hair remains an important area of research in computer graphics. Virtually all available models for scattering off hair or fur fibers are based on separable lobes, which bring practical advantages in importance sampling, but do not represent physically-plausible microgeometry. In this paper, we contribute the first microfacet-based hair scattering model. Based on a rough cylinder geometry with tilted cuticle scales, our far-field model is non-separable by nature, yet allows accurate importance sampling. Additional benefits include support for elliptical hair cross-sections and an analytical solution for the reflected lobe using the GGX distribution. We show that our model captures glint-like forward scattering features in the R lobe that have been observed before but not properly explained.
Temporal Normal Distribution Functions
(The Eurographics Association, 2020) Tessari, Lorenzo; Hanika, Johannes; Dachsbacher, Carsten; Droske, Marc; Dachsbacher, Carsten and Pharr, Matt
Specular aliasing can make seemingly simple scenes notoriously hard to render efficiently: small geometric features with high curvature and near specular reflectance result in tiny lighting features which are difficult to resolve at low sample counts per pixel. LEAN and LEADR mapping can be used to convert geometric surface detail to anisotropic surface roughness in a preprocess. In scenes including fluid simulation this problem is particularly apparent with fast moving elements such as spray particles, which are typically represented as participating media in movie rendering. Both approaches, however, are only valid in the far-field regime where the geometric detail is much smaller than a pixel, while the challenge of resolving highlights remains in the meso-scale. Fast motion and the relatively long shutter intervals, commonly used in movie production, lead to strong variation of the surface normals seen under a pixel over time aggravating the problem. Recent specular anti aliasing approaches preintegrate geometric curvature under the pixel footprint for one specific ray to achieve noise free images at low sample counts. We extend these to anisotropic surface roughness and to account for the temporal surface normal variation due to motion blur. We use temporal derivatives to approximate the distribution of the surface normal seen under a pixel over the course of the shutter interval. Furthermore, we discuss how this can afterwards be combined with the surface BSDF in a practical way.
Markov Chain Mixture Models for Real-Time Direct Illumination
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Dittebrandt, Addis; Schüßler, Vincent; Hanika, Johannes; Herholz, Sebastian; Dachsbacher, Carsten; Ritschel, Tobias; Weidlich, Andrea
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.
Once-more Scattered Next Event Estimation for Volume Rendering
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Hanika, Johannes; Weidlich, Andrea; Droske, Marc; Ghosh, Abhijeet; Wei, Li-Yi
We present a Monte Carlo path tracing technique to sample extended next event estimation contributions in participating media: we consider one additional scattering vertex on the way to the next event, accounting for focused blur, resulting in visually interesting image features. Our technique is tailored to thin homogeneous media with strongly forward scattering phase functions, such as water or atmospheric haze. Previous methods put emphasis on sampling transmittances or geometric factors, and are either limited to isotropic scattering, or used tabulation or polynomial approximation to account for some specific phase functions. We will show how to jointly importance sample the product of an arbitrary phase function with analytic sampling in the solid angle domain and the two reciprocal squared distance terms of the adjacent edges of the transport path. The technique is fast and simple to implement in an existing rendering system. Our estimator is designed specifically for forward scattering, so the new technique has to be combined with other estimators to cover the backward scattering contributions.

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