Abstract We propose a method to accurately handle fluorescence in a non‐spectral (e.g., tristimulus) rendering engine, showcasing color‐shifting and increased luminance effects. Core to our method is a principled reduction technique that encodes the reradiation into a low‐dimensional matrix working in the space of the renderer's Color Matching Functions (CMFs). Our process is independent of a specific CMF set and allows for the addition of a non‐visible ultraviolet band during light transport. Our representation visually matches full spectral light transport for measured fluorescent materials even for challenging illuminants.

Abstract Spectral rendering is essential for the production of physically‐plausible synthetic images, but requires to introduce several changes in the content generation pipeline. In particular, the authoring of spectral material properties (e.g., albedo maps, indices of refraction, transmittance coefficients) raises new problems. While a large panel of computer graphics methods exists to upsample a RGB color to a spectrum, they all provide a one‐to‐one mapping. This limits the ability to control interesting color changes such as the Usambara effect or metameric spectra. In this work, we introduce a one‐to‐many mapping in which we show how we can explore the set of all spectra reproducing a given input color. We apply this method to different colour changing effects such as vathochromism – the change of color with depth, and metamerism.

Abstract In this work, we render in real‐time glittery materials caused by discrete flakes on the surface. To achieve this, one has to count the number of flakes reflecting the light towards the camera within every texel covered by a given pixel footprint. To do so, we derive a counting method for arbitrary footprints that, unlike previous work, outputs the correct statistics. We combine this counting method with an anisotropic parameterization of the texture space that reduces the number of texels falling under a pixel footprint. This allows our method to run with both stable performance and 1.5× to 5× faster than the state‐of‐the‐art.

We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the measure of the distance between two distributions in feature space. The Gram-matrix loss is the ubiquitous approximation for this problem but it is subject to several shortcomings. Our goal is to promote the Sliced Wasserstein Distance as a replacement for it. It is theoretically proven, practical, simple to implement, and achieves results that are visually superior for texture synthesis by optimization or training generative neural networks.

Abstract Recent work has shown that distributing Monte Carlo errors as a blue noise in screen space improves the perceptual quality of rendered images. However, obtaining such distributions remains an open problem with high sample counts and high‐dimensional rendering integrals. In this paper, we introduce a temporal algorithm that aims at overcoming these limitations. Our algorithm is applicable whenever multiple frames are rendered, typically for animated sequences or interactive applications. Our algorithm locally permutes the pixel sequences (represented by their seeds) to improve the error distribution across frames. Our approach works regardless of the sample count or the dimensionality and significantly improves the images in low‐varying screen‐space regions under coherent motion. Furthermore, it adds negligible overhead compared to the rendering times. Note: our supplemental material provides more results with interactive comparisons against previous work.

We derive a novel framework for the efficient analysis and computation of light transport within layered materials. Our derivation consists in two steps. First, we decompose light transport into a set of atomic operators that act on its directional statistics. Specifically, our operators consist of reflection, refraction, scattering, and absorption, whose combinations are sufficient to describe the statistics of light scattering multiple times within layered structures. We show that the first three directional moments (energy, mean and variance) already provide an accurate summary. Second, we extend the adding-doubling method to support arbitrary combinations of such operators efficiently. During shading, we map the directional moments to BSDF lobes. We validate that the resulting BSDF closely matches the ground truth in a lightweight and efficient form. Unlike previous methods we support an arbitrary number of textured layers, and demonstrate a practical and accurate rendering of layered materials with both an offline and real-time implementation that are free from per-material precomputation.

Many applications in rendering rely on integrating functions over spherical polygons. We present a new numerical solution for computing the integral of spherical harmonics (SH) expansions clipped to polygonal domains. Our solution, based on zonal decompositions of spherical integrands and discrete contour integration, introduces an important numerical operating for SH expansions in rendering applications. Our method is simple, efficient, and scales linearly in the bandlimited integrand’s harmonic expansion. We apply our technique to problems in rendering, including surface and volume shading, hierarchical product importance sampling, and fast basis projection for interactive rendering. Moreover, we show how to handle general, nonpolynomial integrands in a Monte Carlo setting using control variates. Our technique computes the integral of bandlimited spherical functions with performance competitive to (or faster than) more general numerical integration methods for a broad class of problems, both in offline and interactive rendering contexts. Our implementation is simple, relying only on self-contained SH evaluation and discrete contour integration routines, and we release a full source CPU-only and shader-based implementations (<750 lines of commented code).

In this work, we introduce an extension to microfacet theory for the rendering of iridescent effects caused by thin-films of varying thickness (such as oil, grease, alcohols, etc) on top of an arbitrarily rough base layer. Our material model is the first to produce a consistent appearance between tristimulus (e.g., RGB) and spectral rendering engines by analytically pre-integrating its spectral response. The proposed extension works with any microfacet-based model: not only on reflection over dielectrics or conductors, but also on transmission through dielectrics. We adapt its evaluation to work in multi-scale rendering contexts, and we expose parameters enabling artistic control over iridescent appearance. The overhead compared to using the classic Fresnel reflectance or transmittance terms remains reasonable enough for practical uses in production.

We present the first method to efficiently predict antialiasing footprints to pre-filter color-, normal-, and displacement-mapped appearance in the context of multi-bounce global illumination. We derive Fourier spectra for radiance and importance functions that allow us to compute spatial-angular filtering footprints at path vertices for both uni- and bi-directional path construction. We then use these footprints to antialias reflectance modulated by high-resolution maps (such as color and normal maps) encountered along a path. In doing so, we also unify the traditional path-space formulation of light transport with our frequency-space interpretation of global illumination pre-filtering. Our method is fully compatible with all existing single bounce pre-filtering appearance models, not restricted by path length, and easy to implement atop existing path-space renderers. We illustrate its effectiveness on several radiometrically complex scenarios where previous approaches either completely fail or require orders of magnitude more time to arrive at similarly high-quality results.

We introduce a novel parameterization for spherical distributions that is based on a point located inside the sphere, which we call a pivot. The pivot serves as the center of a straight-line projection that maps solid angles onto the opposite side of the sphere. By transforming spherical distributions in this way, we derive novel parametric spherical distributions that can be evaluated and importance-sampled from the original distributions using simple, closed-form expressions. Moreover, we prove that if the original distribution can be sampled and/or integrated over a spherical cap, then so can the transformed distribution. We exploit the properties of our parameterization to derive efficient spherical lighting techniques for both real-time and offline rendering. Our techniques are robust, fast, easy to implement, and achieve quality that is superior to previous work.

Rendering participating media requires significant computation, but the effect of volumetric scattering is often eventually smooth. This article proposes an innovative analysis of absorption and scattering of local light fields in the Fourier domain and derives the corresponding set of operators on the covariance matrix of the power spectrum of the light field. This analysis brings an efficient prediction tool for the behavior of light along a light path in participating media. We leverage this analysis to derive proper frequency prediction metrics in 3D by combining per-light path information in the volume. We demonstrate the use of these metrics to significantly improve the convergence of a variety of existing methods for the simulation of multiple scattering in participating media. First, we propose an efficient computation of second derivatives of the fluence, to be used in methods like irradiance caching. Second, we derive proper filters and adaptive sample densities for image-space adaptive sampling and reconstruction. Third, we propose an adaptive sampling for the integration of scattered illumination to the camera. Finally, we improve the convergence of progressive photon beams by predicting where the radius of light gathering can stop decreasing. Light paths in participating media can be very complex. Our key contribution is to show that analyzing local light fields in the Fourier domain reveals the consistency of illumination in such media and provides a set of simple and useful rules to be used to accelerate existing global illumination methods.

The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the covariance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects.

Shading acquired materials with high-frequency illumination is computationally expensive. Estimating the shading integral requires multiple samples of the incident illumination. The number of samples required may vary across the image, and the image itself may have high- and low-frequency variations, depending on a combination of several factors. Adaptively distributing computational budget across the pixels for shading is a challenging problem. In this paper, we depict complex materials such as acquired reflectances, interactively, without any precomputation based on geometry. In each frame, we first estimate the frequencies in the local light field arriving at each pixel, as well as the variance of the shading integrand. Our frequency analysis accounts for combinations of a variety of factors: the reflectance of the object projecting to the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. We then exploit this frequency information (bandwidth and variance) to adaptively sample for reconstruction and integration. For example, fewer pixels per unit area are shaded for pixels projecting onto diffuse objects, and fewer samples are used for integrating illumination incident on specular objects.

Shading complex materials such as acquired reflectances in multi-light environments is computationally expensive. Estimating the shading integral requires multiple samples of the incident illumination. The number of samples required varies across the image, depending on a combination of several factors. Adaptively distributing computational budget across the pixels for shading is a challenging problem. In this paper we depict complex materials such as acquired reflectances, interactively, without any precomputation based on geometry. We first estimate the approximate spatial and angular variation in the local light field arriving at each pixel. This local bandwidth accounts for combinations of a variety of factors: the reflectance of the object projecting to the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. We then exploit this bandwidth information to adaptively sample for reconstruction and integration. For example, fewer pixels per area are shaded for pixels projecting onto diffuse objects, and fewer samples are used for integrating illumination incident on specular objects.