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Item A Low-Dimensional Function Space for Efficient Spectral Upsampling(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jakob, Wenzel; Hanika, Johannes; Alliez, Pierre and Pellacini, FabioShow more We present a versatile technique to convert textures with tristimulus colors into the spectral domain, allowing such content to be used in modern rendering systems. Our method is based on the observation that suitable reflectance spectra can be represented using a low-dimensional parametric model that is intrinsically smooth and energy-conserving, which leads to significant simplifications compared to prior work. The resulting spectral textures are compact and efficient: storage requirements are identical to standard RGB textures, and as few as six floating point instructions are required to evaluate them at any wavelength. Our model is the first spectral upsampling method to achieve zero error on the full sRGB gamut. The technique also supports large-gamut color spaces, and can be vectorized effectively for use in rendering systems that handle many wavelengths at once.Show more Item 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, AndreaShow more 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.Show more Item 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-YiShow more 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.Show more Item 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-YiShow more 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.Show more Item 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, MorganShow more 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.Show more Item 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-YiShow more 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.Show more Item 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, JörgShow more 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.Show more Item Re‐Weighting Firefly Samples for Improved Finite‐Sample Monte Carlo Estimates(© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Zirr, Tobias; Hanika, Johannes; Dachsbacher, Carsten; Chen, Min and Benes, BedrichShow more Samples with high contribution but low probability density, often called fireflies, occur in all practical Monte Carlo estimators and are part of computing unbiased estimates. For finite‐sample estimates, however, they can lead to excessive variance. Rejecting all samples classified as outliers, as suggested in previous work, leads to estimates that are too low and can cause undesirable artefacts. In this paper, we show how samples can be re‐weighted depending on their contribution and sampling frequency such that the finite‐sample estimate gets closer to the correct expected value and the variance can be controlled. For this, we first derive a theory for how samples should ideally be re‐weighted and that this would require the probability density function of the optimal sampling strategy. As this probability density function is generally unknown, we show how the discrepancy between the optimal and the actual sampling strategy can be estimated and used for re‐weighting in practice. We describe an efficient algorithm that allows for the necessary analysis of per‐pixel sample distributions in the context of Monte Carlo rendering without storing any individual samples, with only minimal changes to the rendering algorithm. It causes negligible runtime overhead, works in constant memory and is well suited for parallel and progressive rendering. The re‐weighting runs as a fast post‐process, can be controlled interactively and our approach is non‐destructive in that the unbiased result can be reconstructed at any time.Samples with high contribution but low probability density, often called fireflies, occur in all practical Monte Carlo estimators and are part of computing unbiased estimates. For finite‐sample estimates, however, they can lead to excessive variance. Rejecting all samples classified as outliers, as suggested in previous work, leads to estimates that are too low and can cause undesirable artefacts. In this paper, we show how samples can be re‐weighted depending on their contribution and sampling frequency such that the finite‐sample estimate gets closer to the correct expected value and the variance can be controlled. For this, we first derive a theory for how samples should ideally be re‐weighted and that this would require the probability density function of the optimal sampling strategy. As this probability density function is generally unknown, we show how the discrepancy between the optimal and the actual sampling strategy can be estimated and used for re‐weighting in practice. We describe an efficient algorithm that allows for the necessary analysis of per‐pixel sample distributions in the context of Monte Carlo rendering without storing any individual samples, with only minimal changes to the rendering algorithm.Show more Item Spectral Mollification for Bidirectional Fluorescence(The Eurographics Association and John Wiley & Sons Ltd., 2020) Jung, Alisa; Hanika, Johannes; Dachsbacher, Carsten; Panozzo, Daniele and Assarsson, UlfShow more Fluorescent materials can shift energy between wavelengths, thereby creating bright and saturated colors both in natural and artificial materials. However, rendering fluorescence for continuous wavelengths or combined with wavelength dependent path configurations so far has only been feasible using spectral unidirectional methods. We present a regularization-based approach for supporting fluorescence in a spectral bidirectional path tracer. Our algorithm samples camera and light sub-paths with independent wavelengths, and when connecting them mollifies the BSDF at one of the connecting vertices such that it reradiates light across multiple wavelengths. We discuss arising issues such as color bias in early iterations, consistency of the method and MIS weights in the presence of spectral mollification. We demonstrate our method in scenes combining fluorescence and transport phenomena that are difficult to render with unidirectional or spectrally discrete methods.Show more Item Spectral Rendering with the Bounded MESE and sRGB Data(The Eurographics Association, 2019) Peters, Christoph; Merzbach, Sebastian; Hanika, Johannes; Dachsbacher, Carsten; Klein, Reinhard and Rushmeier, HollyShow more In a recent journal paper, we introduced a technique to represent reflectance spectra by an arbitrary number of Fourier coefficients. As a special case, we converted tristimulus data to three Fourier coefficients. After summarizing this work, we introduce the Fourier sRGB color space. It is defined in terms of Fourier coefficients but designed to behave similar to sRGB. Textures stored in Fourier sRGB support efficient spectral rendering but can be compressed with techniques designed for sRGB textures. Compression errors are similar to sRGB.Show more Item Temporal Normal Distribution Functions(The Eurographics Association, 2020) Tessari, Lorenzo; Hanika, Johannes; Dachsbacher, Carsten; Droske, Marc; Dachsbacher, Carsten and Pharr, MattShow more 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.Show more Item 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, MattShow more 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.Show more Item Wide Gamut Spectral Upsampling with Fluorescence(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jung, Alisa; Wilkie, Alexander; Hanika, Johannes; Jakob, Wenzel; Dachsbacher, Carsten; Boubekeur, Tamy and Sen, PradeepShow more Physically based spectral rendering has become increasingly important in recent years. However, asset textures in such systems are usually still drawn or acquired as RGB tristimulus values. While a number of RGB to spectrum upsampling techniques are available, none of them support upsampling of all colours in the full spectral locus, as it is intrinsically bigger than the gamut of physically valid reflectance spectra. But with display technology moving to increasingly wider gamuts, the ability to achieve highly saturated colours becomes an increasingly important feature. Real materials usually exhibit smooth reflectance spectra, while computationally generated spectra become more blocky as they represent increasingly bright and saturated colours. In print media, plastic or textile design, fluorescent dyes are added to extend the boundaries of the gamut of reflectance spectra. We follow the same approach for rendering: we provide a method which, given an input RGB tristimulus value, automatically provides a mixture of a regular, smooth reflectance spectrum plus a fluorescent part. For highly saturated input colours, the combination yields an improved reconstruction compared to what would be possible relying on a reflectance spectrum alone. At the core of our technique is a simple parametric spectral model for reflectance, excitation, and emission that allows for compact storage and is compatible with texture mapping. The model can then be used as a fluorescent diffuse component in an existing more complex BRDF model. We also provide importance sampling routines for practical application in a path tracer.Show more