Abstract Monte Carlo rendering of translucent objects with heterogeneous scattering properties is often expensive both in terms of memory and computation. If the scattering properties are described by a 3D texture, memory consumption is high. If we do path tracing and use a high dynamic range lighting environment, the computational cost of the rendering can easily become significant. We propose a compact and efficient neural method for representing and rendering the appearance of heterogeneous translucent objects. Instead of assuming only surface variation of optical properties, our method represents the appearance of a full object taking its geometry and volumetric heterogeneities into account. This is similar to a neural radiance field, but our representation works for an arbitrary distant lighting environment. In a sense, we present a version of neural precomputed radiance transfer that captures relighting of heterogeneous translucent objects. We use a multi‐layer perceptron (MLP) with skip connections to represent the appearance of an object as a function of spatial position, direction of observation, and direction of incidence. The latter is considered a directional light incident across the entire non‐self‐shadowed part of the object. We demonstrate the ability of our method to compactly store highly complex materials while having high accuracy when comparing to reference images of the represented object in unseen lighting environments. As compared with path tracing of a heterogeneous light scattering volume behind a refractive interface, our method more easily enables importance sampling of the directions of incidence and can be integrated into existing rendering frameworks while achieving interactive frame rates.

Abstract We present a method for capturing the BSSRDF (bidirectional scattering‐surface reflectance distribution function) of arbitrary geometry with a neural network. We demonstrate how a compact neural network can represent the full 8‐dimensional light transport within an object including heterogeneous scattering. We develop an efficient rendering method using importance sampling that is able to render complex translucent objects under arbitrary lighting. Our method can also leverage the common planar half‐space assumption, which allows it to represent one BSSRDF model that can be used across a variety of geometries. Our results demonstrate that we can render heterogeneous translucent objects under arbitrary lighting and obtain results that match the reference rendered using volumetric path tracing.

Abstract Neural reflectance models are capable of reproducing the spatially‐varying appearance of many real‐world materials at different scales. Unfortunately, existing techniques such as NeuMIP have difficulties handling materials with strong shadowing effects or detailed specular highlights. In this paper, we introduce a neural appearance model that offers a new level of accuracy. Central to our model is an inception‐based core network structure that captures material appearances at multiple scales using parallel‐operating kernels and ensures multi‐stage features through specialized convolution layers. Furthermore, we encode the inputs into frequency space, introduce a gradient‐based loss, and employ it adaptive to the progress of the learning phase. We demonstrate the effectiveness of our method using a variety of synthetic and real examples.

We present a practical method for temporal and stereoscopic filtering that generates stereo-consistent rendering. Existing methods for stereoscopic rendering often reuse samples from one eye for the other or do averaging between the two eyes. These approaches fail in the presence of ray tracing effects such as specular reflections and refractions. We derive a new blending strategy that leverages variance to compute per pixel blending weights for both temporal and stereoscopic rendering. In the temporal domain, our method works well in a low noise context and is robust in the presence of inconsistent motion vectors, where existing methods such as temporal anti-aliasing (TAA) and deep learning super sampling (DLSS) produce artifacts. In the stereoscopic domain, our method provides a new way to ensure consistency between the left and right eyes. The stereoscopic version of our method can be used with our new temporal method or with existing methods such as DLSS and TAA. In all combinations, it reduces the error and significantly increases the consistency between the eyes making it practical for real-time settings such as virtual reality (VR).

Abstract Image denoising based on deep learning has become a powerful tool to accelerate Monte Carlo rendering. Deep learning techniques can produce smooth images using a low sample count. Unfortunately, existing deep learning methods are biased and do not converge to the correct solution as the number of samples increase. In this paper, we propose a progressive denoising technique that aims to use denoising only when it is beneficial and to reduce its impact at high sample counts. We use Stein's unbiased risk estimate (SURE) to estimate the error in the denoised image, and we combine this with a neural network to infer a per‐pixel mixing parameter. We further augment this network with confidence intervals based on classical statistics to ensure consistency and convergence of the final denoised image. Our results demonstrate that our method is consistent and that it improves existing denoising techniques. Furthermore, it can be used in combination with existing high quality denoisers to ensure consistency. In addition to being asymptotically unbiased, progressive denoising is particularly good at preserving fine details that would otherwise be lost with existing denoisers.

Although Monte Carlo path tracing is a simple and effective algorithm to synthesize photo-realistic images, it is often very slow to converge to noise-free results when involving complex global illumination. One of the most successful variance-reduction techniques is path guiding, which can learn better distributions for importance sampling to reduce pixel noise. However, previous methods require a large number of path samples to achieve reliable path guiding. We present a novel neural path guiding approach that can reconstruct high-quality sampling distributions for path guiding from a sparse set of samples, using an offline trained neural network. We leverage photons traced from light sources as the primary input for sampling density reconstruction, which is effective for challenging scenes with strong global illumination. To fully make use of our deep neural network, we partition the scene space into an adaptive hierarchical grid, in which we apply our network to reconstruct high-quality sampling distributions for any local region in the scene. This allows for effective path guiding for arbitrary path bounce at any location in path tracing. We demonstrate that our photon-driven neural path guiding approach can generalize to diverse testing scenes, often achieving better rendering results than previous path guiding approaches and opening up interesting future directions.

Path guiding is a promising technique to reduce the variance of path tracing. Although existing online path guiding algorithms can eventually learn good sampling distributions given a large amount of time and samples, the speed of learning becomes a major bottleneck. In this paper, we accelerate the learning of sampling distributions by training a light-weight neural network offline to reconstruct from sparse samples. Uniquely, we design our neural network to directly operate convolutions on a sparse quadtree, which regresses a high-quality hierarchical sampling distribution. Our approach can reconstruct reasonably accurate sampling distributions faster, allowing for efficient path guiding and rendering. In contrast to the recent offline neural path guiding techniques that reconstruct low-resolution 2D images for sampling, our novel hierarchical framework enables more fine-grained directional sampling with less memory usage, effectively advancing the practicality and efficiency of neural path guiding. In addition, we take advantage of hybrid bidirectional samples including both path samples and photons, as we have found this more robust to different light transport scenarios compared to using only one type of sample as in previous work. Experiments on diverse testing scenes demonstrate that our approach often improves rendering results with better visual quality and lower errors. Our framework can also provide the proper balance of speed, memory cost, and robustness.

Abstract Recently, deep learning‐based denoising approaches have led to dramatic improvements in low sample‐count Monte Carlo rendering. These approaches are aimed at path tracing, which is not ideal for simulating challenging light transport effects like caustics, where photon mapping is the method of choice. However, photon mapping requires very large numbers of traced photons to achieve high‐quality reconstructions. In this paper, we develop the first deep learning‐based method for particle‐based rendering, and specifically focus on photon density estimation, the core of all particle‐based methods. We train a novel deep neural network to predict a kernel function to aggregate photon contributions at shading points. Our network encodes individual photons into per‐photon features, aggregates them in the neighborhood of a shading point to construct a photon local context vector, and infers a kernel function from the per‐photon and photon local context features. This network is easy to incorporate in many previous photon mapping methods (by simply swapping the kernel density estimator) and can produce high‐quality reconstructions of complex global illumination effects like caustics with an order of magnitude fewer photons compared to previous photon mapping methods. Our approach largely reduces the required number of photons, significantly advancing the computational efficiency in photon mapping.

Simulating the appearance of woven fabrics is challenging due to the complex interplay of lighting between the constituent yarns and fibers. Conventional surface-based models lack the fidelity and details for producing realistic close-up renderings. Micro-appearance models, on the other hand, can produce highly detailed renderings by depicting fabrics fiber-by-fiber, but become expensive when handling large pieces of clothing. Further, neither surface-based nor micro-appearance model has not been shown in practice to match measurements of complex anisotropic reflection and transmission simultaneously. In this paper, we introduce a practical appearance model for woven fabrics. We model the structure of a fabric at the ply level and simulate the local appearance of fibers making up each ply. Our model accounts for both reflection and transmission of light and is capable of matching physical measurements better than prior methods including fiber based techniques. Compared to existing micro-appearance models, our model is light-weight and scales to large pieces of clothing.

The bidirectional reflectance distribution function (BRDF) is crucial for modeling the appearance of real-world materials. In production rendering, analytic BRDF models are often used to approximate the surface appearance since they are compact and flexible. Measured BRDFs usually have a more realistic appearance, but consume much more storage and are hard to modify. In this paper, we propose a novel framework for connecting measured and analytic BRDFs. First, we develop a robust method for separating a measured BRDF into diffuse and specular components. This is commonly done in analytic models, but has been difficult previously to do explicitly for measured BRDFs. This diffuse-specular separation allows novel measured BRDF editing on the diffuse and specular parts separately. In addition, we conduct analysis on each part of the measured BRDF, and demonstrate a more intuitive and lower-dimensional PCA model than Nielsen et al. [2015]. In fact, our measured BRDF model has the same number of parameters (8 parameters) as the commonly used analytic models, such as the GGX model. Finally, we visualize the analytic and measured BRDFs in the same space, and directly demonstrate their similarities and differences. We also design an analytic fitting algorithm for two-lobe materials, which is more robust, efficient and simple, compared to previous non-convex optimization-based analytic fitting methods.

Physically-based fur rendering is difficult. Recently, structural differences between hair and fur fibers have been revealed by Yan et al. (2015), who showed that fur fibers have an inner scattering medulla, and developed a double cylinder model. However, fur rendering is still complicated due to the complex scattering paths through the medulla. We develop a number of optimizations that improve efficiency and generality without compromising accuracy, leading to a practical fur reflectance model. We also propose a key contribution to support both near and far-field rendering, and allow smooth transitions between them. Specifically, we derive a compact BCSDF model for fur reflectance with only 5 lobes. Our model unifies hair and fur rendering, making it easy to implement within standard hair rendering software, since we keep the traditional R , TT , and TRT lobes in hair, and only add two extensions to scattered lobes, TT s and TRT s . Moreover, we introduce a compression scheme using tensor decomposition to dramatically reduce the precomputed data storage for scattered lobes to only 150 KB, with minimal loss of accuracy. By exploiting piecewise analytic integration, our method further enables a multi-scale rendering scheme that transitions between near and far field rendering smoothly and efficiently for the first time, leading to 6 -- 8× speed up over previous work.

Physically-based hair and fur rendering is crucial for visual realism. One of the key effects is global illumination, involving light bouncing between different fibers. This is very time-consuming to simulate with methods like path tracing. Efficient approximate global illumination techniques such as dual scattering are in widespread use, but are limited to human hair only, and cannot handle color bleeding, transparency and hair-object inter-reflection. We present the first global illumination model, based on dipole diffusion for subsurface scattering, to approximate light bouncing between individual fur fibers. We model complex light and fur interactions as subsurface scattering, and use a simple neural network to convert from fur fibers' properties to scattering parameters. Our network is trained on only a single scene with different parameters, but applies to general scenes and produces visually accurate appearance, supporting color bleeding and further inter-reflections.

We develop a method to acquire the BRDF of a homogeneous flat sample from only two images, taken by a near-field perspective camera, and lit by a directional light source. Our method uses the MERL BRDF database to determine the optimal set of lightview pairs for data-driven reflectance acquisition. We develop a mathematical framework to estimate error from a given set of measurements, including the use of multiple measurements in an image simultaneously, as needed for acquisition from near-field setups. The novel error metric is essential in the near-field case, where we show that using the condition-number alone performs poorly. We demonstrate practical near-field acquisition of BRDFs from only one or two input images. Our framework generalizes to configurations like a fixed camera setup, where we also develop a simple extension to spatially-varying BRDFs by clustering the materials.

The bidirectional reflectance distribution function (BRDF) is critical for rendering, and accurate material representation requires data-driven reflectance models. However, isotropic BRDFs are 3D functions, and measuring the reflectance of a flat sample can require a million incident and outgoing direction pairs, making the use of measured BRDFs impractical. In this paper, we address the problem of reconstructing a measured BRDF from a limited number of samples. We present a novel mapping of the BRDF space, allowing for extraction of descriptive principal components from measured databases, such as the MERL BRDF database. We optimize for the best sampling directions, and explicitly provide the optimal set of incident and outgoing directions in the Rusinkiewicz parameterization for n = {1, 2, 5, 10, 20} samples. Based on the principal components, we describe a method for accurately reconstructing BRDF data from these limited sets of samples. We validate our results on the MERL BRDF database, including favorable comparisons to previous sets of industry-standard sampling directions, as well as with BRDF measurements of new flat material samples acquired with a gantry system. As an extension, we also demonstrate how this method can be used to find optimal sampling directions when imaging a sphere of a homogeneous material; in this case, only two images are often adequate for high accuracy.

Rendering photo-realistic animal fur is a long-standing problem in computer graphics. Considerable effort has been made on modeling the geometric complexity of fur, but the reflectance of fur fibers is not well understood. Fur has a distinct diffusive and saturated appearance, that is not captured by either the Marschner hair model or the Kajiya-Kay model. In this paper, we develop a physically-accurate reflectance model for fur fibers. Based on anatomical literature and measurements, we develop a double cylinder model for the reflectance of a single fur fiber, where an outer cylinder represents the biological observation of a cortex covered by multiple cuticle layers, and an inner cylinder represents the scattering interior structure known as the medulla. Our key contribution is to model medulla scattering accurately---in contrast, for human hair, the medulla has minimal width and thus negligible contributions to the reflectance. Medulla scattering introduces additional reflection and transmission paths, as well as diffusive reflectance lobes. We validate our physical model with measurements on real fur fibers, and introduce the first database in computer graphics of reflectance profiles for nine fur samples. We show that our model achieves significantly better fits to the measured data than the Marschner hair reflectance model. For efficient rendering, we develop a method to precompute 2D medulla scattering profiles and analytically approximate our reflectance model with factored lobes. The accuracy of the approach is validated by comparing our rendering model to full 3D light transport simulations. Our model provides an enriched set of controls, where the parameters we fit can be directly used to render realistic fur, or serve as a starting point from which artists can manually tune parameters for desired appearances.

Abstract We present a novel appearance model for paper. Based on our appearance measurements for matte and glossy paper, we find that paper exhibits a combination of subsurface scattering, specular reflection, retroreflection, and surface sheen. Classic microfacet and simple diffuse reflection models cannot simulate the double‐sided appearance of a thin layer. Our novel BSDF model matches our measurements for paper and accounts for both reflection and transmission properties. At the core of the BSDF model is a method for converting a multi‐layer subsurface scattering model (BSSRDF) into a BSDF, which allows us to retain physically‐based absorption and scattering parameters obtained from the measurements. We also introduce a method for computing the amount of light available for subsurface scattering due to transmission through a rough dielectric surface. Our final model accounts for multiple scattering, single scattering, and surface reflection and is capable of rendering paper with varying levels of roughness and glossiness on both sides.

This article introduces a practical shading model for cloth that can simulate both anisotropic highlights as well as the complex color shifts seen in cloth made of different colored threads. Our model is based on extensive Bidirectional Reflectance Distribution Function (BRDF) measurements of several cloth samples. We have also measured the scattering profile of several different individual cloth threads. Based on these measurements, we derived an empirical shading model capable of predicting the light scattering profile of a variety of threads. From individual threads, we synthesized a woven cloth model, which provides an intuitive description of the layout of the constituent threads as well as their tangent directions. Our model is physically plausible, accounting for shadowing and masking by the threads. We validate our model by comparing predicted and measured light scattering values and show how it can reproduce the appearance of many cloth and thread types, including silk, velvet, linen, and polyester. The model is robust, easy to use, and can simulate the appearance of complex highlights and color shifts that cannot be fully handled by existing models.

We present a new sampling space for light transport paths that makes it possible to describe Monte Carlo path integration and photon density estimation in the same framework. A key contribution of our paper is the introduction of vertex perturbations, which extends the space of paths with loosely coupled connections. The new framework enables the computation of path probabilities in the same space under the same measure, which allows us to use multiple importance sampling to combine Monte Carlo path integration and photon density estimation. The resulting algorithm, unified path sampling , can robustly render complex combinations and glossy surfaces and caustics that are problematic for existing light transport simulation methods.

We investigate global illumination in 2D and show how this simplified problem domain leads to practical insights for 3D rendering. We first derive a full theory of 2D light transport by introducing 2D analogs to radiometric quantities such as flux and radiance, and deriving a 2D rendering equation. We use our theory to show how to implement algorithms such as Monte Carlo raytracing, path tracing, irradiance caching, and photon mapping in 2D, and demonstrate that these algorithms can be analyzed more easily in this domain while still providing insights for 3D rendering. We apply our theory to develop several practical improvements to the irradiance caching algorithm. We perform a full second-order analysis of diffuse indirect illumination, first in 2D, and then in 3D by deriving the irradiance Hessian, and show how this leads to increased accuracy and performance for irradiance caching. We propose second-order Taylor expansion from cache points, which results in more accurate irradiance reconstruction. We also introduce a novel error metric to guide cache point placement by analyzing the error produced by irradiance caching. Our error metric naturally supports anisotropic reconstruction and, in our preliminary study, resulted in an order of magnitude less error than the “split-sphere” heuristic when using the same number of cache points.

In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops.

This paper introduces a new error metric for irradiance caching that significantly outperforms the classic Split-Sphere heuristic. Our new error metric builds on recent work using second order gradients (Hessians) as a principled error bound for the irradiance. We add occlusion information to the Hessian computation, which greatly improves the accuracy of the Hessian in complex scenes, and this makes it possible for the first time to use a radiometric error metric for irradiance caching. We enhance the metric making it based on the relative error in the irradiance as well as robust in the presence of black occluders. The resulting error metric is efficient to compute, numerically robust, supports elliptical error bounds and arbitrary hemispherical sample distributions, and unlike the Split-Sphere heuristic it is not necessary to arbitrarily clamp the computed error thresholds. Our results demonstrate that the new error metric outperforms existing error metrics based on the Split-Sphere model and occlusion-unaware Hessians.

We present a new adaptive photon tracing algorithm which can handle illumination settings that are considered difficult for photon tracing approaches such as outdoor scenes, close-ups of a small part of an illuminated region, and illumination coming through a small gap. The key contribution in our algorithm is the use of visibility of photon path as the importance function which ensures that our sampling algorithm focuses on paths that are visible from the given viewpoint. Our sampling algorithm builds on two recent developments in Markov chain Monte Carlo methods: adaptive Markov chain sampling and replica exchange. Using these techniques, each photon path is adaptively mutated and it explores the sampling space efficiently without being stuck at a local peak of the importance function. We have implemented this sampling approach in the progressive photon mapping algorithm which provides visibility information in a natural way when a photon path contributes to a measurement point. We demonstrate that the final algorithm is strikingly simple, yet effective at sampling photons under lighting conditions that would be difficult for existing Monte Carlo ray tracing-based methods.

We present two contributions to the area of volumetric rendering. We develop a novel, comprehensive theory of volumetric radiance estimation that leads to several new insights and includes all previously published estimates as special cases. This theory allows for estimating in-scattered radiance at a point, or accumulated radiance along a camera ray, with the standard photon particle representation used in previous work. Furthermore, we generalize these operations to include a more compact, and more expressive intermediate representation of lighting in participating media, which we call “photon beams.” The combination of these representations and their respective query operations results in a collection of nine distinct volumetric radiance estimates. Our second contribution is a more efficient rendering method for participating media based on photon beams. Even when shooting and storing less photons and using less computation time, our method significantly reduces both bias (blur) and variance in volumetric radiance estimation. This enables us to render sharp lighting details (e.g., volume caustics) using just tens of thousands of photon beams, instead of the millions to billions of photon points required with previous methods.

Accurate global illumination rendering using GPUs is gaining attention because of the highly parallel nature of global illumination algorithms. For example, computing the radiance of each pixel using path tracing is embarrassingly parallel. Some major commercial rendering software also started adopting global illumination on GPUs.

We present an error estimation framework for progressive photon mapping. Although estimating rendering error has been established for unbiased rendering algorithms, error estimation for biased rendering algorithms has not been investigated well in comparison. We characterize the error by the sum of a bias estimate and a stochastic noise bound, which is motivated by stochastic error bounds formulation in biased methods. As a part of our error computation, we extend progressive photon mapping to operate with smooth kernels. This enables the calculation of illumination gradients with arbitrary accuracy, which we use to progressively compute the local bias in the radiance estimate. We also show how variance can be computed in progressive photon mapping, which is used to estimate the error due to noise. As an example application, we show how our error estimation can be used to compute images with a given error threshold. For this example application, our framework only requires the error threshold and a confidence level to automatically terminate rendering. Our results demonstrate how our error estimation framework works well in realistic synthetic scenes.

Rendering hair in motion pictures is an important and challenging task. Despite much research on physically based hair rendering, it is currently difficult to benefit from this work because physically based shading models do not offer artist friendly controls. As a consequence much production work so far has used ad hoc shaders that are easier to control, but often lack the richness seen in real hair. We show that physically based shading models fail to provide intuitive artist controls and we introduce a novel approach for creating an art-directable hair shading model from existing physically based models. Through an informal user study we show that this system is easier to use compared to existing systems. Our shader has been integrated into the production pipeline at the Walt Disney Animation Studios and is being used in the production of the upcoming animated feature film Tangled.

Abstract In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a by‐product of the sampling procedure we produce a multi‐resolution representation of the density function as either a spherical mip‐map or Haar wavelet. By exploiting this implicit conversion we can extend the method to distribute samples according to the product of an SH function with a spherical mip‐map or Haar wavelet. This generalization has immediate applicability in rendering, e.g., importance sampling the product of a BRDF and an environment map where the lighting is stored as a single high‐resolution wavelet and the BRDF is represented in spherical harmonics. Since spherical harmonics can be efficiently rotated, this product can be computed on‐the‐fly even if the BRDF is stored in local‐space. Our sampling approach generates over 6 million samples per second while significantly reducing precomputation time and storage requirements compared to previous techniques.

We present a new model of the homogeneous BSSRDF based on large-scale simulations. Our model captures the appearance of materials that are not accurately represented using existing single scattering models or multiple isotropic scattering models (e.g. the diffusion approximation). We use an analytic function to model the 2D hemispherical distribution of exitant light at a point on the surface, and a table of parameter values of this function computed at uniformly sampled locations over the remaining dimensions of the BSSRDF domain. This analytic function is expressed in elliptic coordinates and has six parameters which vary smoothly with surface position, incident angle, and the underlying optical properties of the material (albedo, mean free path length, phase function and the relative index of refraction). Our model agrees well with measured data, and is compact, requiring only 250MB to represent the full spatial- and angular-distribution of light across a wide spectrum of materials. In practice, rendering a single material requires only about 100KB to represent the BSSRDF.

This paper presents a simple extension of progressive photon mapping for simulating global illumination with effects such as depth-of-field, motion blur, and glossy reflections. Progressive photon mapping is a robust global illumination algorithm that can handle complex illumination settings including specular-diffuse-specular paths. The algorithm can compute the correct radiance value at a point in the limit. However, progressive photon mapping is not effective at rendering distributed ray tracing effects, such as depth-of-field, that requires multiple pixel samples in order to compute the correct average radiance value over a region. In this paper, we introduce a new formulation of progressive photon mapping, called stochastic progressive photon mapping, which makes it possible to compute the correct average radiance value for a region. The key idea is to use shared photon statistics within the region rather than isolated photon statistics at a point. The algorithm is easy to implement, and our results demonstrate how it efficiently handles scenes with distributed ray tracing effects, while maintaining the robustness of progressive photon mapping in scenes with complex lighting.

Abstract We present a new method for efficiently simulating the scattering of light within participating media. Using a theoretical reformulation of volumetric photon mapping, we develop a novel photon gathering technique for participating media. Traditional volumetric photon mapping samples the in‐scattered radiance at numerous points along the length of a single ray by performing costly range queries within the photon map. Our technique replaces these multiple point‐queries with a single beam‐query, which explicitly gathers all photons along the length of an entire ray. These photons are used to estimate the accumulated in‐scattered radiance arriving from a particular direction and need to be gathered only once per ray. Our method handles both fixed and adaptive kernels, is faster than regular volumetric photon mapping, and produces images with less noise.

Abstract In this paper we present a technique for computing translational gradients of indirect surface reflectance in scenes containing participating media and significant occlusions. These gradients describe how the incident radiance field changes with respect to translation on surfaces. Previous techniques for computing gradients ignore the effects of volume scattering and attenuation and assume that radiance is constant along rays connecting surfaces. We present a novel gradient formulation that correctly captures the influence of participating media. Our formulation accurately accounts for changes of occlusion, including the effect of surfaces occluding scattering media. We show how the proposed gradients can be used within an irradiance caching framework to more accurately handle scenes with participating media, providing significant improvements in interpolation quality.

We present a new adaptive sampling strategy for ray tracing. Our technique is specifically designed to handle multidimensional sample domains, and it is well suited for efficiently generating images with effects such as soft shadows, motion blur, and depth of field. These effects are problematic for existing image based adaptive sampling techniques as they operate on pixels, which are possibly noisy results of a Monte Carlo ray tracing process. Our sampling technique operates on samples in the multidimensional space given by the rendering equation and as a consequence the value of each sample is noise-free. Our algorithm consists of two passes. In the first pass we adaptively generate samples in the multidimensional space, focusing on regions where the local contrast between samples is high. In the second pass we reconstruct the image by integrating the multidimensional function along all but the image dimensions. We perform a high quality anisotropic reconstruction by determining the extent of each sample in the multidimensional space using a structure tensor. We demonstrate our method on scenes with a 3 to 5 dimensional space, including soft shadows, motion blur, and depth of field. The results show that our method uses fewer samples than Mittchell's adaptive sampling technique while producing images with less noise.

This paper introduces a simple and robust progressive global illumination algorithm based on photon mapping. Progressive photon mapping is a multi-pass algorithm where the first pass is ray tracing followed by any number of photon tracing passes. Each photon tracing pass results in an increasingly accurate global illumination solution that can be visualized in order to provide progressive feedback. Progressive photon mapping uses a new radiance estimate that converges to the correct radiance value as more photons are used. It is not necessary to store the full photon map, and unlike standard photon mapping it possible to compute a global illumination solution with any desired accuracy using a limited amount of memory. Compared with existing Monte Carlo ray tracing methods progressive photon mapping provides an efficient and robust alternative in the presence of complex light transport such as caustics and in particular reflections of caustics.

In this article we present a novel radiance caching method for efficiently rendering participating media using Monte Carlo ray tracing. Our method handles all types of light scattering including anisotropic scattering, and it works in both homogeneous and heterogeneous media. A key contribution in the article is a technique for computing gradients of radiance evaluated in participating media. These gradients take the full path of the scattered light into account including the changing properties of the medium in the case of heterogeneous media. The gradients can be computed simultaneously with the inscattered radiance with negligible overhead. We compute gradients for single scattering from lights and surfaces and for multiple scattering, and we use a spherical harmonics representation in media with anisotropic scattering. Our second contribution is a new radiance caching scheme for participating media. This caching scheme uses the information in the radiance gradients to sparsely sample as well as interpolate radiance within the medium utilizing a novel, perceptually based error metric. Our method provides several orders of magnitude speedup compared to path tracing and produces higher quality results than volumetric photon mapping. Furthermore, it is view-driven and well suited for large scenes where methods such as photon mapping become costly.

Abstract Why is the sky blue? Why is grass green? What determines the color of human skin? Questions such as these are increasingly important in the development of the next generation algorithms for appearancemodeling in computer graphics. By closely simulating the natural world around us we can develop algorithms that are useful in areas not traditionally connected with computer graphics. An example could be the ability to predict the color of human skin in the presence of certain diseases. In this talk, I will describe some of our recentwork in simulating the appearance of materials such as human skin, milk, and ice. This includes new research for predicting the appearance of materials based on their molecular structure in order to answer the question: “what will it look like if I mix these molecules together”?

This paper introduces a theoretical model for computing the scattering properties of participating media and translucent materials. The model takes as input a description of the components of a medium and computes all the parameters necessary to render it. These parameters are the extinction and scattering coefficients, the phase function, and the index of refraction, Our theory is based on a robust generalization of the Lorenz-Mie theory. Previous models using Lorenz-Mie theory have been limited to non-absorbing media with spherical particles such as paints and clouds. Our generalized theory is capable of handling both absorbing host media and non-spherical particles, which significantly extends the classes of media and materials that can be modeled. We use the theory to computer optical properties for different types of ice and ocean water, and we derive a novel appearance model for milk parameterized by the fat and protein contents. Our results show that we are able to match measured scattering properties in cases where the classical Lorez-Mie theory breaks down, and we can compute properties for media that cannot be measured using existing techniques in computer graphics.

The visual world around us displays a rich set of volumetric effects due to participating media. The appearance of these media is governed by several physical properties such as particle densities, shapes and sizes, which must be input (directly or indirectly) to a rendering algorithm to generate realistic images. While there has been significant progress in developing rendering techniques (for instance, volumetric Monte Carlo methods and analytic approximations), there are very few methods that measure or estimate these properties for media that are of relevance to computer graphics. In this paper, we present a simple device and technique for robustly estimating the properties of a broad class of participating media that can be either (a) diluted in water such as juices, beverages, paints and cleaning supplies, or (b) dissolved in water such as powders and sugar/salt crystals, or (c) suspended in water such as impurities. The key idea is to dilute the concentrations of the media so that single scattering effects dominate and multiple scattering becomes negligible, leading to a simple and robust estimation algorithm. Furthermore, unlike previous approaches that require complicated or separate measurement setups for different types or properties of media, our method and setup can be used to measure media with a complete range of absorption and scattering properties from a single HDR photograph. Once the parameters of the diluted medium are estimated, a volumetric Monte Carlo technique may be used to create renderings of any medium concentration and with multiple scattering. We have measured the scattering parameters of forty commonly found materials, that can be immediately used by the computer graphics community. We can also create realistic images of combinations or mixtures of the original measured materials, thus giving the user a wide flexibility in making realistic images of participating media.

We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and -- since we do not use the original measured data -- easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis.

We present a new technique for importance sampling products of complex functions using wavelets. First, we generalize previous work on wavelet products to higher dimensional spaces and show how this product can be sampled on-the-fly without the need of evaluating the full product. This makes it possible to sample products of high-dimensional functions even if the product of the two functions in itself is too memory consuming. Then, we present a novel hierarchical sample warping algorithm that generates high-quality point distributions, which match the wavelet representation exactly. One application of the new sampling technique is rendering of objects with measured BRDFs illuminated by complex distant lighting --- our results demonstrate how the new sampling technique is more than an order of magnitude more efficient than the best previous techniques.

This paper introduces a shading model for light diffusion in multi-layered translucent materials. Previous work on diffusion in translucent materials has assumed smooth semi-infinite homogeneous materials and solved for the scattering of light using a dipole diffusion approximation. This approximation breaks down in the case of thin translucent slabs and multi-layered materials. We present a new efficient technique based on multiple dipoles to account for diffusion in thin slabs. We enhance this multipole theory to account for mismatching indices of refraction at the top and bottom of of translucent slabs, and to model the effects of rough surfaces. To model multiple layers, we extend this single slab theory by convolving the diffusion profiles of the individual slabs. We account for multiple scattering between slabs by using a variant of Kubelka-Munk theory in frequency space. Our results demonstrate diffusion of light in thin slabs and multi-layered materials such as paint, paper, and human skin.

This paper introduces a new method for real-time relighting of scenes illuminated by local light sources. We extend previous work on precomputed radiance transfer for distant lighting to local lighting by introducing the concept of unstructured light clouds. The unstructured light cloud enables a compact representation of local lights in the model and real-time rendering of complex models with full global illumination due to local light sources. We use simplification of lights, and clustered PCA to obtain a compressed representation. When storing only the indirect component of the illumination, we are able to get high quality with only 8-16 lighting coefficients per vertex. Our results demonstrate real-time rendering of scenes with moving lights, dynamic cameras, glossy materials and global illumination.

The appearance of computer generated plants has improved significantly due to advances in both modeling and rendering. In this paper we describe a system that further improves the appearance of CG plants by including the tiny hairs that cover many plant organs. A plant skeleton is generated using an L-system and graphically interpreted using generalized cylinders. The individual hairs are then mapped onto the surfaces and boundary edges of the mesh. Hair properties are specified and adjusted according to positional information. Sample images included in the paper illustrate the impact of hairs on the appearance of rendered plants.

We introduce structured importance sampling , a new technique for efficiently rendering scenes illuminated by distant natural illumination given in an environment map. Our method handles occlusion, high-frequency lighting, and is significantly faster than alternative methods based on Monte Carlo sampling. We achieve this speedup as a result of several ideas. First, we present a new metric for stratifying and sampling an environment map taking into account both the illumination intensity as well as the expected variance due to occlusion within the scene. We then present a novel hierarchical stratification algorithm that uses our metric to automatically stratify the environment map into regular strata. This approach enables a number of rendering optimizations, such as pre-integrating the illumination within each stratum to eliminate noise at the cost of adding bias, and sorting the strata to reduce the number of sample rays. We have rendered several scenes illuminated by natural lighting, and our results indicate that structured importance sampling is better than the best previous Monte Carlo techniques, requiring one to two orders of magnitude fewer samples for the same image quality.

Light scattering from hair is normally simulated in computer graphics using Kajiya and Kay's classic phenomenological model. We have made new measurements of scattering from individual hair fibers that exhibit visually significant effects not predicted by Kajiya and Kay's model. Our measurements go beyond previous hair measurements by examining out-of-plane scattering, and together with this previous work they show a multiple specular highlight and variation in scattering with rotation about the fiber axis. We explain the sources of these effects using a model of a hair fiber as a transparent elliptical cylinder with an absorbing interior and a surface covered with tilted scales. Based on an analytical scattering function for a circular cylinder, we propose a practical shading model for hair that qualitatively matches the scattering behavior shown in the measurements. In a comparison between a photograph and rendered images, we demonstrate the new model's ability to match the appearance of real hair.

This paper introduces an efficient two-pass rendering technique for translucent materials. We decouple the computation of irradianceat the surface from the evaluation of scattering inside the material.This is done by splitting the evaluation into two passes, where the first pass consists of computing the irradiance at selected points on the surface. The second pass uses a rapid hierarchical integration technique to evaluate a diffusion approximation based on the irradiance samples. This approach is substantially faster than previous methods for rendering translucent materials, and it has the advantage that it integrates seamlessly with both scanline rendering and global illumination methods. We show several images and animations from our implementation that demonstrate that the approach is both fast and robust, making it suitable for rendering translucent materials in production.

We present a physically based method for modeling and animating fire. Our method is suitable for both smooth (laminar) and turbulent flames, and it can be used to animate the burning of either solid or gas fuels. We use the incompressible Navier-Stokes equations to independently model both vaporized fuel and hot gaseous products. We develop a physically based model for the expansion that takes place when a vaporized fuel reacts to form hot gaseous products, and a related model for the similar expansion that takes place when a solid fuel is vaporized into a gaseous state. The hot gaseous products, smoke and soot rise under the influence of buoyancy and are rendered using a blackbody radiation model. We also model and render the blue core that results from radicals in the chemical reaction zone where fuel is converted into products. Our method allows the fire and smoke to interact with objects, and flammable objects can catch on fire.

In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the inter-action of smoke with moving objects.

This paper presents a physically-based model of the night sky for realistic image synthesis. We model both the direct appearance of the night sky and the illumination coming from the Moon, the stars, the zodiacal light, and the atmosphere. To accurately predict the appearance of night scenes we use physically-based astronomical data, both for position and radiometry. The Moon is simulated as a geometric model illuminated by the Sun, using recently measured elevation and albedo maps, as well as a specialized BRDF. For visible stars, we include the position, magnitude, and temperature of the star, while for the Milky Way and other nebulae we use a processed photograph. Zodiacal light due to scattering in the dust covering the solar system, galactic light, and airglow due to light emission of the atmosphere are simulated from measured data. We couple these components with an accurate simulation of the atmosphere. To demonstrate our model, we show a variety of night scenes rendered with a Monte Carlo ray tracer.

This paper introduces a simple model for subsurface light transport in translucent materials. The model enables efficient simulation of effects that BRDF models cannot capture, such as color bleeding within materials and diffusion of light across shadow boundaries. The technique is efficient even for anisotropic, highly scattering media that are expensive to simulate using existing methods. The model combines an exact solution for single scattering with a dipole point source diffusion approximation for multiple scattering. We also have designed a new, rapid image-based measurement technique for determining the optical properties of translucent materials. We validate the model by comparing predicted and measured values and show how the technique can be used to recover the optical properties of a variety of materials, including milk, marble, and skin. Finally, we describe sampling techniques that allow the model to be used within a conventional ray tracer.

Article Free Access Share on Modeling and rendering of weathered stone Authors: Julie Dorsey Laboratory for Computer Science, Massachusetts Institute of Technology Laboratory for Computer Science, Massachusetts Institute of TechnologyView Profile , Alan Edelman Laboratory for Computer Science, Massachusetts Institute of Technology Laboratory for Computer Science, Massachusetts Institute of TechnologyView Profile , Henrik Wann Jensen Laboratory for Computer Science, Massachusetts Institute of Technology Laboratory for Computer Science, Massachusetts Institute of TechnologyView Profile , Justin Legakis Laboratory for Computer Science, Massachusetts Institute of Technology Laboratory for Computer Science, Massachusetts Institute of TechnologyView Profile , Hans Køhling Pedersen Laboratory for Computer Science, Massachusetts Institute of Technology Laboratory for Computer Science, Massachusetts Institute of TechnologyView Profile Authors Info & Claims SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniquesJuly 1999 Pages 225–234https://doi.org/10.1145/311535.311560Online:01 July 1999Publication History 176citation1,637DownloadsMetricsTotal Citations176Total Downloads1,637Last 12 Months6Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Article Efficient simulation of light transport in scenes with participating media using photon maps Share on Authors: Henrik Wann Jensen mental images, Berlin, Germany mental images, Berlin, GermanyView Profile , Per H. Christensen mental images, Berlin, Germany mental images, Berlin, GermanyView Profile Authors Info & Claims SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniquesJuly 1998 Pages 311–320https://doi.org/10.1145/280814.280925Online:24 July 1998Publication History 245citation5,023DownloadsMetricsTotal Citations245Total Downloads5,023Last 12 Months92Last 6 weeks12 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

This paper presents a new technique for rendering caustics on non‐Lambertian surfaces. The method is based on an extension of the photon map which removes previous restrictions limiting the usage to Lambertian surfaces. We add information about the incoming direction to the photons and this allows us to combine the photon map with arbitrary reflectance functions. By using a cone‐filter we improve the quality of the radiance estimate in particular at discontinuities. Furthermore we introduce balancing of the photon map which not only reduces the memory requirements but also significantly reduces the rendering time. We have used the method to render caustics on surfaces with reflectance functions varying from Lambertian to glossy specular.