Importance Sampling Spherical Harmonics

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.     

Practical Product Importance Sampling for Direct Illumination

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet‐based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF on‐the‐fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree‐based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.     

Bidirectional Importance Sampling for Unstructured Direct Illumination

Recent research in bidirectional importance sampling has focused primarily on structured illumination sources such as distant environment maps, while unstructured illumination has received little attention. In this paper, we present a method for bidirectional importance sampling of unstructured illumination, allowing us to use the same method for sampling both distant as well as local/indirect sources. Building upon recent work in [ WFA*05 ], we model complex illumination as a large set of point lights. The subsequent sampling process draws samples only from this point set. We start by constructing a piecewise constant approximation for the lighting using an illumination cut [ CPWAP08 ]. We show that this cut can be used directly for illumination importance sampling. We then use BRDF importance sampling followed by sample counting to update the cut, resulting in a bidirectional distribution that closely approximates the product of the illumination and BRDF. Drawing visibility samples from this new distribution significantly reduces the sampling variance. As a main advance over previous work, our method allows for unstructured sources, including arbitrary local direct lighting and one-bounce of indirect lighting.     

Anisotropic Radiance-Cache Splatting for Efficiently Computing High-Quality Global Illumination with Lightcuts

Computing global illumination in complex scenes is even with todays computational power a demanding task. In this work we propose a novel irradiance caching scheme that combines the advantages of two state-of-the-art algorithms for high-quality global illumination rendering: lightcuts , an adaptive and hierarchical instant-radiosity based algorithm and the widely used (ir)radiance caching algorithm for sparse sampling and interpolation of (ir)radiance in object space. Our adaptive radiance caching algorithm is based on anisotropic cache splatting, which adapts the cache footprints not only to the magnitude of the illumination gradient computed with light-cuts but also to its orientation allowing larger interpolation errors along the direction of coherent illumination while reducing the error along the illumination gradient. Since lightcuts computes the direct and indirect lighting seamlessly, we use a two-layer radiance cache, to store and control the interpolation of direct and indirect lighting individually with different error criteria. In multiple iterations our method detects cache interpolation errors above the visibility threshold of a pixel and reduces the anisotropic cache footprints accordingly. We achieve significantly better image quality while also speeding up the computation costs by one to two orders of magnitude with respect to the well-known photon mapping with (ir)radiance caching procedure.     

Portal‐Masked Environment Map Sampling

We present a technique to efficiently importance sample distant, all‐frequency illumination in indoor scenes. Standard environment sampling is inefficient in such cases since the distant lighting is typically only visible through small openings (e.g. windows). This visibility is often addressed by manually placing a portal around each window to direct samples towards the openings; however, uniformly sampling the portal (its area or solid angle) disregards the possibly high frequency environment map. We propose a new portal importance sampling technique which takes into account both the environment map and its visibility through the portal, drawing samples proportional to the product of the two. To make this practical, we propose a novel, portal‐rectified reparametrization of the environment map with the key property that the visible region induced by a rectangular portal projects to an axis‐aligned rectangle. This allows us to sample according to the desired product distribution at an arbitrary shading location using a single (precomputed) summed‐area table per portal. Our technique is unbiased, relevant to many renderers, and can also be applied to rectangular light sources with directional emission profiles, enabling efficient rendering of non‐diffuse light sources with soft shadows.     

From Faces to Outdoor Light Probes

Image‐based lighting has allowed the creation of photo‐realistic computer‐generated content. However, it requires the accurate capture of the illumination conditions, a task neither easy nor intuitive, especially to the average digital photography enthusiast. This paper presents an approach to directly estimate an HDR light probe from a single LDR photograph, shot outdoors with a consumer camera, without specialized calibration targets or equipment. Our insight is to use a person's face as an outdoor light probe. To estimate HDR light probes from LDR faces we use an inverse rendering approach which employs data‐driven priors to guide the estimation of realistic, HDR lighting. We build compact, realistic representations of outdoor lighting both parametrically and in a data‐driven way, by training a deep convolutional autoencoder on a large dataset of HDR sky environment maps. Our approach can recover high‐frequency, extremely high dynamic range lighting environments. For quantitative evaluation of lighting estimation accuracy and relighting accuracy, we also contribute a new database of face photographs with corresponding HDR light probes. We show that relighting objects with HDR light probes estimated by our method yields realistic results in a wide variety of settings.     

Inverse lighting design using a coverage optimization strategy

Lighting design is an essential process in computer cinematography, games, architectural design and various other applications for correctly illuminating or highlighting parts of a scene and enhancing storytelling. When targeting specific illumination goals and constraints, this process can be tedious and counter-intuitive even for experienced users and thus automatic, goal-driven methods have emerged for the estimation of a lighting configuration to match the desired result. We present a general automatic approach to such an inverse lighting design problem, where the number of light sources along with their position and emittance are computed given a set of user-specified lighting goals. To this end, we employ a special hierarchical light clustering that operates in the lighting goal coverage domain and overcomes limitations of previous approaches in environments with high occlusion or structural complexity. Our approach is independent of the underlying light transport model and can quickly converge to usable solutions. We validate our results and provide comparative evaluation with the current state of the art.     

Fast Soft Self‐Shadowing on Dynamic Height Fields

We present a new, real‐time method for rendering soft shadows from large light sources or lighting environments on dynamic height fields. The method first computes a horizon map for a set of azimuthal directions. To reduce sampling, we compute a multi‐resolution pyramid on the height field. Coarser pyramid levels are indexed as the distance from caster to receiver increases. For every receiver point and every azimuthal direction, a smooth function of blocking angle in terms of log distance is reconstructed from a height difference sample at each pyramid level. This function's maximum approximates the horizon angle. We then sum visibility at each receiver point over wedges determined by successive pairs of horizon angles. Each wedge represents a linear transition in blocking angle over its azimuthal extent. It is precomputed in the order‐4 spherical harmonic (SH) basis, for a canonical azimuthal origin and fixed extent, resulting in a 2D table. The SH triple product of 16D vectors representing lighting, total visibility, and diffuse reflectance then yields the soft‐shadowed result. Two types of light sources are considered; both are distant and low‐frequency. Environmental lights require visibility sampling around the complete 360 ° azimuth, while key lights sample visibility within a partial swath. Restricting the swath concentrates samples where the light comes from (e.g. 3 azimuthal directions vs. 16‐32 for a full swath) and obtains sharper shadows. Our GPU implementation handles height fields up to 1024 × 1024 in real‐time. The computation is simple, local, and parallel, with performance independent of geometric content.     

Exploratory Stage Lighting Design using Visual Objectives

Lighting is a critical element of theater. A lighting designer is responsible for drawing the audience's attention to a specific part of the stage, setting time of day, creating a mood, and conveying emotions. Designers often begin the lighting design process by collecting reference visual imagery that captures different aspects of their artistic intent. Then, they experiment with various lighting options to determine which ideas work best on stage. However, modern stages contain tens to hundreds of lights, and setting each light source's parameters individually to realize an idea is both tedious and requires expert skill. In this paper, we describe an exploratory lighting design tool based on feedback from professional designers. The system extracts abstract visual objectives from reference imagery and applies them to target regions of the stage. Our system can rapidly generate plausible design candidates that embody the visual objectives through a Gibbs sampling method, and present them as a design gallery for rapid exploration and iterative refinement. We demonstrate that the resulting system allows lighting designers of all skill levels to quickly create and communicate complex designs, even for scenes containing many color‐changing lights.     

Appearance Sampling of Real Objects for Variable Illumination

The appearance of an object greatly changes under different lighting conditions. Even so, previous studies have demonstrated that the appearance of an object under varying illumination conditions can be represented by a linear subspace. A set of basis images spanning such a linear subspace can be obtained by applying the principal component analysis (PCA) for a large number of images taken under different lighting conditions. Since little is known about how to sample the appearance of an object in order to correctly obtain its basis images, it was a common practice to use as many input images as possible. In this study, we present a novel method for analytically obtaining a set of basis images of an object for varying illumination from input images of the object taken properly under a set of light sources, such as point light sources or extended light sources. Our proposed method incorporates the sampling theorem of spherical harmonics for determining a set of lighting directions to efficiently sample the appearance of an object. We further consider the issue of aliasing caused by insufficient sampling of the object's appearance. In particular, we investigate the effectiveness of using extended light sources for modeling the appearance of an object under varying illumination without suffering the aliasing caused by insufficient sampling of its appearance.     

From few to many: illumination cone models for face recognitionunder variable lighting and pose

We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render (or synthesize) images of the face under novel poses and illumination conditions. The pose space is then sampled and, for each pose, the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone. Test results show that the method performs almost without error, except on the most extreme lighting directions     

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.     

Interactive Lighting Design with Hierarchical Light Representation

Lighting design plays a crucial role in indoor lighting design, computer cinematograph and many other applications. Computer‐assisted lighting design aims to find a lighting configuration that best approximates the illumination effect specified by designers. In this paper, we present an automatic approach for lighting design, in which discrete and continuous optimization of the lighting configuration, including the number, intensity, and position of lights, are achieved. Our lighting design algorithm consists of two major steps. The first step estimates an initial lighting configuration by light sampling and clustering. The initial light clusters are then recursively merged to form a light hierarchy. The second step optimizes the lighting configuration by alternatively selecting a light cut on the light hierarchy to determine the number of representative lights and optimizing the lighting parameters using the simplex method. To speed up the optimization computation, only illumination at scene vertices that are important to rendering are sampled and taken into account in the optimization. Using the proposed approach, we develop a lighting design system that can compute appropriate lighting configurations to generate the illumination effects iteratively painted and modified by a designer interactively.     

Exploiting Visibility Correlation in Direct Illumination

The visibility function in direct illumination describes the binary visibility over a light source, e.g., an environment map. Intuitively, the visibility is often strongly correlated between nearby locations in time and space, but exploiting this correlation without introducing noticeable errors is a hard problem. In this paper, we first study the statistical characteristics of the visibility function. Then, we propose a robust and unbiased method for using estimated visibility information to improve the quality of Monte Carlo evaluation of direct illumination. Our method is based on the theory of control variates, and it can be used on top of existing state‐of‐the‐art schemes for importance sampling. The visibility estimation is obtained by sparsely sampling and caching the 4D visibility field in a compact bitwise representation. In addition to Monte Carlo rendering, the stored visibility information can be used in a number of other applications, for example, ambient occlusion and lighting design.     

Visualization of Particle‐based Data with Transparency and Ambient Occlusion

Particle‐based simulation techniques, like the discrete element method or molecular dynamics, are widely used in many research fields. In real‐time explorative visualization it is common to render the resulting data using opaque spherical glyphs with local lighting only. Due to massive overlaps, however, inner structures of the data are often occluded rendering visual analysis impossible. Furthermore, local lighting is not sufficient as several important features like complex shapes, holes, rifts or filaments cannot be perceived well. To address both problems we present a new technique that jointly supports transparency and ambient occlusion in a consistent illumination model. Our approach is based on the emission‐absorption model of volume rendering. We provide analytic solutions to the volume rendering integral for several density distributions within a spherical glyph. Compared to constant transparency our approach preserves the three‐dimensional impression of the glyphs much better. We approximate ambient illumination with a fast hierarchical voxel cone‐tracing approach, which builds on a new real‐time voxelization of the particle data. Our implementation achieves interactive frame rates for millions of static or dynamic particles without any preprocessing. We illustrate the merits of our method on real‐world data sets gaining several new insights.     

Practical Product Sampling by Fitting and Composing Warps

We introduce a Monte Carlo importance sampling method for integrands composed of products and show its application to rendering where direct sampling of the product is often difficult. Our method is based on warp functions that operate on the primary samples in [0,1)ⁿ, where each warp approximates sampling a single factor of the product distribution. Our key insight is that individual factors are often well-behaved and inexpensive to fit and sample in primary sample space, which leads to a practical, efficient sampling algorithm. Our sampling approach is unbiased, easy to implement, and compatible with multiple importance sampling. We show the results of applying our warps to projected solid angle sampling of spherical triangles, to sampling bilinear patch light sources, and to sampling glossy BSDFs and area light sources, with efficiency improvements of over 1.6× on real-world scenes.     

Image-space hierarchical coherence buffer

Indirect illumination plays an important role in global illumination. However, computing indirect illumination is a time-consuming process and needs to be approximated to achieve interactive performance. Indirect illumination varies rather slowly across the surface. This leads to the idea of computing indirect illumination sparsely in the scene and interpolating the result. This paper presents a hierarchical structure, which enables efficient sampling. The hierarchy is constructed in the image space by exploiting coherences among the screen-space pixels. From the hierarchy, samples are chosen, each of which represents a group of coherent pixels. This paper presents two methods of utilizing the samples for indirect lighting computation. The methods produce plausible lighting results and show high performances. The proposed algorithms run entirely in the image space and are easy to implement in contemporary graphic hardware.     

Outlier deletion based improvement on the StOMP algorithm for sparse solution of large-scale underdetermined problems

StOMP algorithm is well suited to large-scale underdetermined applications in sparse vector estimations. It can reduce computation complexity and has some attractive asymptotical statistical properties.However,the estimation speed is at the cost of accuracy violation. This paper suggests an improvement on the StOMP algorithm that is more efficient in finding a sparse solution to the large-scale underdetermined problems. Also,compared with StOMP,this modified algorithm can not only more accurately estimate parameters for the distribution of matched filter coefficients,but also improve estimation accuracy for the sparse vector itself. Theoretical success boundary is provided based on a large-system limit for approximate recovery of sparse vector by modified algorithm,which validates that the modified algorithm is more efficient than StOMP. Actual computations with simulated data show that without significant increment in computation time,the proposed algorithm can greatly improve the estimation accuracy.     

Combining Point and Line Samples for Direct Illumination

We develop a unified framework for combining point and line samples in direct lighting calculations. While line samples have proven beneficial in a variety of rendering contexts, their application in direct lighting has been limited due to a lack of formulas for evaluating advanced BRDFs along a line and performance tied to the orientation of occluders in the scene. We lift these limitations by elevating line samples to a shared higher‐dimensional space with point samples. Our key insight is to separate the probability distribution functions of line samples and points that lie along a line sample. This simple conceptual change allows us to apply multiple importance sampling (MIS) between points and lines, and lines with each other, in order to leverage their respective strengths. We also show how to improve the convergence rate of MIS between points and lines in an unbiased way using a novel discontinuity‐smoothing balance heuristic. We verify through a set of rendering experiments that our proposed MISing of points and lines, and lines with each other, reduces variance of the direct lighting estimate while supporting an increased range of BSDFs compared to analytic line integration.     

Importance Sampling Techniques for Path Tracing in Participating Media

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we decouple ray marching from light calculations by computing a representation of the transmittance function that can be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per‐ray memory requirements and does not require any preprocessing, making it simple to integrate into production ray tracing based renderers.