Product Importance Sampling for Light Transport Path Guiding

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.     

Flux‐Limited Diffusion for Multiple Scattering in Participating Media

For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non‐physical radiative fluxes which leads to a poor match to correct light transport. In particular, this prevents the application of classical diffusion approximation to heterogeneous media, where opaque material is embedded within transparent regions. To address this limitation, we introduce flux‐limited diffusion, a technique from the astrophysics domain. This method provides a better approximation to light transport than classical diffusion approximation, particularly when applied to heterogeneous media, and hence broadens the applicability of diffusion‐based techniques. We provide an algorithm for flux‐limited diffusion, which is validated using the transport theory for a point light source in an infinite homogeneous medium. We further demonstrate that our implementation of flux‐limited diffusion produces more accurate renderings of multiple scattering in various heterogeneous datasets than classical diffusion approximation, by comparing both methods to ground truth renderings obtained via volumetric path tracing.     

Accurate Translucent Material Rendering under Spherical Gaussian Lights

In this paper we present a new algorithm for accurate rendering of translucent materials under Spherical Gaussian (SG) lights. Our algorithm builds upon the quantized‐diffusion BSSRDF model recently introduced in [ [dI11] ]. Our main contribution is an efficient algorithm for computing the integral of the BSSRDF with an SG light. We incorporate both single and multiple scattering components. Our model improves upon previous work by accounting for the incident angle of each individual SG light. This leads to more accurate rendering results, notably elliptical profiles from oblique illumination. In contrast, most existing models only consider the total irradiance received from all lights, hence can only generate circular profiles. Experimental results show that our method is suitable for rendering of translucent materials under finite‐area lights or environment lights that can be approximated by a small number of SGs.     

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

Traditionally, Lagrangian fields such as finite‐time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view‐dependent Monte Carlo‐based approach for the visualization of such Lagrangian fields in time‐dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high‐quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high‐quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real‐world numerical simulations.     

Pre‐convolved Radiance Caching

The incident indirect light over a range of image pixels is often coherent. Two common approaches to exploit this inter‐pixel coherence to improve rendering performance are Irradiance Caching and Radiance Caching. Both compute incident indirect light only for a small subset of pixels (the cache), and later interpolate between pixels. Irradiance Caching uses scalar values that can be interpolated efficiently, but cannot account for shading variations caused by normal and reflectance variation between cache items. Radiance Caching maintains directional information, e.g., to allow highlights between cache items, but at the cost of storing and evaluating a Spherical Harmonics (SH) function per pixel. The arithmetic and bandwidth cost for this evaluation is linear in the number of coefficients and can be substantial. In this paper, we propose a method to replace it by an efficient per‐cache item pre‐filtering based on MIP maps — such as previously done for environment maps — leading to a single constant‐time lookup per pixel. Additionally, per‐cache item geometry statistics stored in distance‐MIP maps are used to improve the quality of each pixel's lookup. Our approximate interactive global illumination approach is an order of magnitude faster than Radiance Caching with Phong BRDFs and can be combined with Monte Carlo‐raytracing, Point‐based Global Illumination or Instant Radiosity.     

An Area‐Preserving Parametrization for Spherical Rectangles

We present an area‐preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]² and range in a region included in the unit‐radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]² onto the spherical rectangle. This allows for easily incorporating stratified, quasi‐Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.     

Sample‐Based Manifold Filtering for Interactive Global Illumination and Depth of Field

We present a fast reconstruction filtering method for images generated with Monte Carlo–based rendering techniques. Our approach specializes in reducing global illumination noise in the presence of depth‐of‐field effects at very low sampling rates and interactive frame rates. We employ edge‐aware filtering in the sample space to locally improve outgoing radiance of each sample. The improved samples are then distributed in the image plane using a fast, linear manifold‐based approach supporting very large circles of confusion. We evaluate our filter by applying it to several images containing noise caused by Monte Carlo–simulated global illumination, area light sources and depth of field. We show that our filter can efficiently denoise such images at interactive frame rates on current GPUs and with as few as 4–16 samples per pixel. Our method operates only on the colour and geometric sample information output of the initial rendering process. It does not make any assumptions on the underlying rendering technique and sampling strategy and can therefore be implemented completely as a post‐process filter.     

Convolution‐Based Simulation of Homogeneous Subsurface Scattering

This paper introduces a new method for simulating homogeneous subsurface light transport in translucent objects. Our approach is based on irradiance convolutions over a multi‐layered representation of the volume for light transport, which is general enough to obtain plausible depictions of translucent objects based on the diffusion approximation. We aim at providing an efficient physically based algorithm that can apply arbitrary diffusion profiles to general geometries. We obtain accurate results for a wide range of materials, on par with the hierarchical method by Jensen and Buhler.     

ISHair: Importance Sampling for Hair Scattering

We present an importance sampling method for the bidirectional scattering distribution function (bsdf) of hair. Our method is based on the multi‐lobe hair scattering model presented by Sadeghi et al. [ [SPJT10] ]. We reduce noise by drawing samples from a distribution that approximates the bsdf well. Our algorithm is efficient and easy to implement, since the sampling process requires only the evaluation of a few analytic functions, with no significant memory overhead or need for precomputation. We tested our method in a research raytracer and a production renderer based on micropolygon rasterization. We show significant improvements for rendering direct illumination using multiple importance sampling and for rendering indirect illumination using path tracing.     

Multiple Scattering Approximation in Heterogeneous Media by Narrow Beam Distributions

Fast realistic rendering of objects in scattering media is still a challenging topic in computer graphics. In presence of participating media, a light beam is repeatedly scattered by media particles, changing direction and getting spread out. Explicitly evaluating this beam distribution would enable efficient simulation of multiple scattering events without involving costly stochastic methods. Narrow beam theory provides explicit equations that approximate light propagation in a narrow incident beam. Based on this theory, we propose a closed‐form distribution function for scattered beams. We successfully apply it to the image synthesis of scenes in which scattering occurs, and show that our proposed estimation method is more accurate than those based on the Wentzel‐Kramers‐Brillouin (WKB) theory.     

Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Guided Image Filtering for Interactive High‐quality Global Illumination

Interactive computation of global illumination is a major challenge in current computer graphics research. Global illumination heavily affects the visual quality of generated images. It is therefore a key attribute for the perception of photo‐realistic images. Path tracing is able to simulate the physical behaviour of light using Monte Carlo techniques. However, the computational burden of this technique prohibits interactive rendering times on standard commodity hardware in high‐quality. Trying to solve the Monte Carlo integration with fewer samples results in characteristic noisy images. Global illumination filtering methods take advantage of the fact that the integral for neighbouring pixels may be very similar. Averaging samples of similar characteristics in screen‐space may approximate the correct integral, but may result in visible outliers. In this paper, we present a novel path tracing pipeline based on an edge‐aware filtering method for the indirect illumination which produces visually more pleasing results without noticeable outliers. The key idea is not to filter the noisy path traced images but to use it as a guidance to filter a second image composed from characteristic scene attributes that do not contain noise by default. We show that our approach better approximates the Monte Carlo integral compared to previous methods. Since the computation is carried out completely in screen‐space it is therefore applicable to fully dynamic scenes, arbitrary lighting and allows for high‐quality path tracing at interactive frame rates on commodity hardware.     

Analytic Tangent Irradiance Environment Maps for Anisotropic Surfaces

Environment‐mapped rendering of Lambertian isotropic surfaces is common, and a popular technique is to use a quadratic spherical harmonic expansion. This compact irradiance map representation is widely adopted in interactive applications like video games. However, many materials are anisotropic, and shading is determined by the local tangent direction, rather than the surface normal. Even for visualization and illustration, it is increasingly common to define a tangent vector field, and use anisotropic shading. In this paper, we extend spherical harmonic irradiance maps to anisotropic surfaces, replacing Lambertian reflectance with the diffuse term of the popular Kajiya‐Kay model. We show that there is a direct analogy, with the surface normal replaced by the tangent. Our main contribution is an analytic formula for the diffuse Kajiya‐Kay BRDF in terms of spherical harmonics; this derivation is more complicated than for the standard diffuse lobe. We show that the terms decay even more rapidly than for Lambertian reflectance, going as l^–3, where l is the spherical harmonic order, and with only 6 terms (l = 0 and l = 2) capturing 99.8% of the energy. Existing code for irradiance environment maps can be trivially adapted for real‐time rendering with tangent irradiance maps. We also demonstrate an application to offline rendering of the diffuse component of fibers, using our formula as a control variate for Monte Carlo sampling.     

Interactive cloth rendering of microcylinder appearance model under environment lighting

This paper proposes an interactive rendering method of cloth fabrics under environment lighting. The outgoing radiance from cloth fabrics in the microcylinder model is calculated by integrating the product of the distant environment lighting, the visibility function, the weighting function that includes shadowing/masking effects of threads, and the light scattering function of threads. The radiance calculation at each shading point of the cloth fabrics is simplified to a linear combination of triple product integrals of two circular Gaussians and the visibility function, multiplied by precomputed spherical Gaussian convolutions of the weighting function. We propose an efficient calculation method of the triple product of two circular Gaussians and the visibility function by using the gradient of signed distance function to the visibility boundary where the binary visibility changes in the angular domain of the hemisphere. Our GPU implementation enables interactive rendering of static cloth fabrics with dynamic viewpoints and lighting. In addition, interactive editing of parameters for the scattering function (e.g. thread's albedo) that controls the visual appearances of cloth fabrics can be achieved.     

Boundary‐Aware Extinction Mapping

We introduce Boundary‐Aware Extinction Maps for interactive rendering of massive heterogeneous volumetric datasets. Our approach is based on the projection of the extinction along light rays into a boundary‐aware function space, focusing on the most relevant sections of the light paths. This technique also provides an alternative representation of the set of participating media, allowing scattering simulation methods to be applied on arbitrary volume representations. Combined with a simple out‐of‐core rendering framework, Boundary‐Aware Extinction Maps are valuable tools for interactive applications as well as production previsualization and rendering.     

A Biophysically‐Based Model of the Optical Properties of Skin Aging

This paper presents a time‐varying, multi‐layered biophysically‐based model of the optical properties of human skin, suitable for simulating appearance changes due to aging. We have identified the key aspects that cause such changes, both in terms of the structure of skin and its chromophore concentrations, and rely on the extensive medical and optical tissue literature for accurate data. Our model can be expressed in terms of biophysical parameters, optical parameters commonly used in graphics and rendering (such as spectral absorption and scattering coefficients), or more intuitively with higher‐level parameters such as age, gender, skin care or skin type. It can be used with any rendering algorithm that uses diffusion profiles, and it allows to automatically simulate different types of skin at different stages of aging, avoiding the need for artistic input or costly capture processes. While the presented skin model is inspired on tissue optics studies, we also provided a simplified version valid for non‐diagnostic applications.     

RBF Volume Ray Casting on Multicore and Manycore CPUs

Modern supercomputers enable increasingly large N‐body simulations using unstructured point data. The structures implied by these points can be reconstructed implicitly. Direct volume rendering of radial basis function (RBF) kernels in domain‐space offers flexible classification and robust feature reconstruction, but achieving performant RBF volume rendering remains a challenge for existing methods on both CPUs and accelerators. In this paper, we present a fast CPU method for direct volume rendering of particle data with RBF kernels. We propose a novel two‐pass algorithm: first sampling the RBF field using coherent bounding hierarchy traversal, then subsequently integrating samples along ray segments. Our approach performs interactively for a range of data sets from molecular dynamics and astrophysics up to 82 million particles. It does not rely on level of detail or subsampling, and offers better reconstruction quality than structured volume rendering of the same data, exhibiting comparable performance and requiring no additional preprocessing or memory footprint other than the BVH. Lastly, our technique enables multi‐field, multi‐material classification of particle data, providing better insight and analysis.     

Approximate Bias Compensation for Rendering Scenes with Heterogeneous Participating Media

In this paper we present a novel method for high‐quality rendering of scenes with participating media. Our technique is based on instant radiosity, which is used to approximate indirect illumination between surfaces by gathering light from a set of virtual point lights (VPLs). It has been shown that this principle can be applied to participating media as well, so that the combined single scattering contribution of VPLs within the medium yields full multiple scattering. As in the surface case, VPL methods for participating media are prone to singularities, which appear as bright “splotches” in the image. These artifacts are usually countered by clamping the VPLs' contribution, but this leads to energy loss within the short‐distance light transport. Bias compensation recovers the missing energy, but previous approaches are prohibitively costly. We investigate VPL‐based methods for rendering scenes with participating media, and propose a novel and efficient approximate bias compensation technique. We evaluate our technique using various test scenes, showing it to be visually indistinguishable from ground truth.     

Visualization of Large‐Scale Urban Models through Multi‐Level Relief Impostors

In this paper, we present an efficient approach for the interactive rendering of large‐scale urban models, which can be integrated seamlessly with virtual globe applications. Our scheme fills the gap between standard approaches for distant views of digital terrains and the polygonal models required for close‐up views. Our work is oriented towards city models with real photographic textures of the building facades. At the heart of our approach is a multi‐resolution tree of the scene defining multi‐level relief impostors. Key ingredients of our approach include the pre‐computation of a small set of zenithal and oblique relief maps that capture the geometry and appearance of the buildings inside each node, a rendering algorithm combining relief mapping with projective texture mapping which uses only a small subset of the pre‐computed relief maps, and the use of wavelet compression to simulate two additional levels of the tree. Our scheme runs considerably faster than polygonal‐based approaches while producing images with higher quality than competing relief‐mapping techniques. We show both analytically and empirically that multi‐level relief impostors are suitable for interactive navigation through large urban models.     

Higher Order Ray Marching

Rendering participating media is still a challenging and time consuming task. In such media light interacts at every differential point of its path. Several rendering algorithms are based on ray marching: dividing the path of light into segments and calculating interactions at each of them. In this work, we revisit and analyze ray marching both as a quadrature integrator and as an initial value problem solver, and apply higher order adaptive solvers that ensure several interesting properties, such as faster convergence, adaptiveness to the mathematical definition of light transport and robustness to singularities. We compare several numerical methods, including standard ray marching and Monte Carlo integration, and illustrate the benefits of different solvers for a variety of scenes. Any participating media rendering algorithm that is based on ray marching may benefit from the application of our approach by reducing the number of needed samples (and therefore, rendering time) and increasing accuracy.