An Analysis of the In‐Out BRDF Factorization for View‐Dependent Relighting

Interactive rendering with dynamic natural lighting and changing view is a long‐standing goal in computer graphics. Recently, precomputation‐based methods for all‐frequency relighting have made substantial progress in this direction. Many of the most successful algorithms are based on a factorization of the BRDF into incident and outgoing directions, enabling each term to be precomputed independent of viewing direction, and re‐combined at run‐time. However, there has so far been no theoretical understanding of the accuracy of this factorization, nor the number of terms needed. In this paper, we conduct a theoretical and empirical analysis of the BRDF in‐out factorization. For Phong BRDFs, we obtain analytic results, showing that the number of terms needed grows linearly with the Phong exponent, while the factors correspond closely to spherical harmonic basis functions. More generally, the number of terms is quadratic in the frequency content of the BRDF along the reflected or half‐angle direction. This analysis gives clear practical guidance on the number of factors needed for a given material. Different objects in a scene can each be represented with the correct number of terms needed for that particular BRDF, enabling both accuracy and interactivity.     

Interactive Editing of Lighting and Materials using a Bivariate BRDF Representation

We present a new Precomputed Radiance Transfer (PRT) algorithm based on a two dimensional representation of isotropic BRDFs. Our approach involves precomputing matrices that allow quickly mapping environment lighting, which is represented in the global coordinate system, and the surface BRDFs, which are represented in a bivariate domain, to the local hemisphere at a surface location where the reflection integral is evaluated. When the lighting and BRDFs are represented in a wavelet basis, these rotation matrices are sparse and can be efficiently stored and combined with pre‐computed visibility at run‐time. Compared to prior techniques that also precompute wavelet rotation matrices, our method allows full control over the lighting and materials due to the way the BRDF is represented. Furthermore, this bivariate parameterization preserves sharp specular peaks and grazing effects that are attenuated in conventional parameterizations. We demonstrate a prototype rendering system that achieves real‐time framerates while lighting and materials are edited.     

Interactive Diffraction from Biological Nanostructures

We describe a technique for interactive rendering of diffraction effects produced by biological nanostructures, such as snake skin surface gratings. Our approach uses imagery from atomic force microscopy that accurately captures the geometry of the nanostructures responsible for structural colouration, that is, colouration due to wave interference, in a variety of animals. We develop a rendering technique that constructs bidirectional reflection distribution functions (BRDFs) directly from the measured data and leverages pre‐computation to achieve interactive performance. We demonstrate results of our approach using various shapes of the surface grating nanostructures. Finally, we evaluate the accuracy of our pre‐computation‐based technique and compare to a reference BRDF construction technique     

Minimal Sampling for Effective Acquisition of Anisotropic BRDFs

BRDFs are commonly used for material appearance representation in applications ranging from gaming and the movie industry, to product design and specification. Most applications rely on isotropic BRDFs due to their better availability as a result of their easier acquisition process. On the other hand, anisotropic BRDF due to their structure‐dependent anisotropic highlights, are more challenging to measure and process. This paper thus leverages the measurement process of anisotropic BRDF by representing such BRDF by the collection of isotropic BRDFs. Our method relies on an anisotropic BRDF database decomposition into training isotropic slices forming a linear basis, where appropriate sparse samples are identified using numerical optimization. When an unknown anisotropic BRDF is measured, these samples are repeatably captured in a small set of azimuthal directions. All collected samples are then used for an entire measured BRDF reconstruction from a linear isotropic basis. Typically, below 100 samples are sufficient for the capturing of main visual features of complex anisotropic materials, and we provide a minimal directional samples to be regularly measured at each sample rotation. We conclude, that even simple setups relying on five bidirectional samples (maximum of five stationary sensors/lights) in combination with eight rotations (rotation stage for specimen) can yield a promising reconstruction of anisotropic behavior. Next, we outline extension of the proposed approach to adaptive sampling of anisotropic BRDF to gain even better performance. Finally, we show that our method allows using standard geometries, including industrial multi‐angle reflectometers, for the fast measurement of anisotropic BRDFs.     

Optimizing BRDF orientations for the manipulation of anisotropic highlights

This paper introduces a system for the direct editing of highlights produced by anisotropic BRDFs, which we call anisotropic highlights. We first provide a comprehensive analysis of the link between the direction of anisotropy and the shape of highlight curves for arbitrary object surfaces. The gained insights provide the required ingredients to infer BRDF orientations from a prescribed highlight tangent field. This amounts to a non‐linear optimization problem, which is solved at interactive framerates during manipulation. Taking inspiration from sculpting software, we provide tools that give the impression of manipulating highlight curves while actually modifying their tangents. Our solver produces desired highlight shapes for a host of lighting environments and anisotropic BRDFs.     

g‐BRDFs: An Intuitive and Editable BTF Representation

Measured reflection data such as the bidirectional texture function (BTF) represent spatial variation under the full hemisphere of view and light directions and offer a very realistic visual appearance. Despite its high‐dimensional nature, recent compression techniques allow rendering of BTFs in real time. Nevertheless, a still unsolved problem is that there is no representation suited for real‐time rendering that can be used by designers to modify the BTF's appearance. For intuitive editing, a set of low‐dimensional comprehensible parameters, stored as scalars, colour values or texture maps, is required. In this paper we present a novel way to represent BTF data by introducing the geometric BRDF (g‐BRDF), which describes both the underlying meso‐ and micro‐scale structure in a very compact way. Both are stored in texture maps with only a few additional scalar parameters that can all be modified at runtime and thus give the designer full control over the material's appearance in the final real‐time application. The g‐BRDF does not only allow intuitive editing, but also reduces the measured data into a small set of textures, yielding a very effective compression method. In contrast to common material representation combining heightfields and BRDFs, our g‐BRDF is physically based and derived from direct measurement, thus representing real‐world surface appearance. In addition, we propose an algorithm for fully automatic decomposition of a given measured BTF into the g‐BRDF representation.     

Real-time editing and relighting of homogeneous translucent materials

Existing techniques for fast, high-quality rendering of translucent materials often fix BSSRDF parameters at precomputation time. We present a novel method for accurate rendering and relighting of translucent materials that also enables real-time editing and manipulation of homogeneous diffuse BSSRDFs. We first apply PCA analysis on diffuse multiple scattering to derive a compact basis set, consisting of only twelve 1D functions. We discovered that this small basis set is accurate enough to approximate a general diffuse scattering profile. For each basis, we then precompute light transport data representing the translucent transfer from a set of local illumination samples to each rendered vertex. This local transfer model allows our system to integrate a variety of lighting models in a single framework, including environment lighting, local area lights, and point lights. To reduce the PRT data size, we compress both the illumination and spatial dimensions using efficient nonlinear wavelets. To edit material properties in real-time, a user-defined diffuse BSSRDF is dynamically projected onto our precomputed basis set, and is then multiplied with the translucent transfer information on the fly. Using our system, we demonstrate realistic, real-time translucent material editing and relighting effects under a variety of complex, dynamic lighting scenarios.     

Template‐Based Sampling of Anisotropic BRDFs

BRDFs are commonly used to represent given materials’ appearance in computer graphics and related fields. Although, in the recent past, BRDFs have been extensively measured, compressed, and fitted by a variety of analytical models, most research has been primarily focused on simplified isotropic BRDFs. In this paper, we present a unique database of 150 BRDFs representing a wide range of materials; the majority exhibiting anisotropic behavior. Since time‐consuming BRDF measurement represents a major obstacle in the digital material appearance reproduction pipeline, we tested several approaches estimating a very limited set of samples capable of high quality appearance reconstruction. Initially, we aligned all measured BRDFs according to the location of the anisotropic highlights. Then we propose an adaptive sampling method based on analysis of the measured BRDFs. For each BRDF, a unique sampling pattern was computed, given a predefined count of samples. Further, template‐based methods are introduced based on reusing of the precomputed sampling patterns. This approach enables a more efficient measurement of unknown BRDFs while preserving the visual fidelity for the majority of tested materials. Our method exhibits better performance and stability than competing sparse sampling approaches; especially for higher numbers of samples.     

Efficient Reflectance and Visibility Approximations for Environment Map Rendering

We present a technique for approximating isotropic BRDFs and precomputed self-occlusion that enables accurate and efficient prefiltered environment map rendering. Our approach uses a nonlinear approximation of the BRDF as a weighted sum of isotropic Gaussian functions. Our representation requires a minimal amount of storage, can accurately represent BRDFs of arbitrary sharpness, and is above all, efficient to render. We precompute visibility due to self-occlusion and store a low-frequency approximation suitable for glossy reflections. We demonstrate our method by fitting our representation to measured BRDF data, yielding high visual quality at real-time frame rates.     

Realtime Rendering Glossy to Glossy Reflections in Screen Space

Glossy to glossy reflections are lights bounced between glossy surfaces. Such directional light transports are important for humans to perceive glossy materials, but difficult to simulate. This paper proposes a new method for rendering screen‐space glossy to glossy reflections in realtime. We use spherical von Mises‐Fisher (vMF) distributions to model glossy BRDFs at surfaces, and employ screen space directional occlusion (SSDO) rendering framework to trace indirect light transports bounced in the screen space. As our main contributions, we derive a new parameterization of vMF distribution so as to convert the non‐linear fit of multiple vMF distributions into a linear sum in the new space. Then, we present a new linear filtering technique to build MIP‐maps on glossy BRDFs, which allows us to create filtered radiance transfer functions at runtime, and efficiently estimate indirect glossy to glossy reflections. We demonstrate our method in a realtime application for rendering scenes with dynamic glossy objects. Compared with screen space directional occlusion, our approach only requires one extra texture and has a negligible overhead, 3% ～ 6% loss at frame rate, but enables glossy to glossy reflections.     

Spatial Directional Radiance Caching

We present a new approach for accelerated global illumination computation in scenes with glossy surfaces. Our algorithm combines sparse illumination computation used in the radiance caching algorithm with BRDF importance sampling. To make this approach feasible, we extend the idea of lazy illumination evaluation, used in the caching approaches, from the spatial to the directional domain. Using importance sampling allows us to apply caching not only on low-gloss but also on shiny materials with high-frequency BRDFs, for which the radiance caching algorithm breaks down.     

Fast Estimation and Rendering of Indirect Highlights

This paper proposes a method for efficiently rendering indirect highlights. Indirect highlights are caused by the primary light source reflecting off two or more glossy surfaces. Accurately simulating such highlights is important to convey the realistic appearance of materials such as chrome and shiny metal. Our method models the glossy BRDF at a surface point as a directional distribution, using a spherical von Mises‐Fisher (vMF) distribution. As our main contribution, we merge multiple vMFs into a combined multimodal distribution. This effectively creates a filtered radiance response function, allowing us to efficiently estimate indirect highlights. We demonstrate our method in a near‐interactive application for rendering scenes with highly glossy objects. Our results produce realistic reflections under both local and environment lighting.     

A General BRDF Representation Based on Tensor Decomposition

Generating photo‐realistic images through Monte Carlo rendering requires efficient representation of light–surface interaction and techniques for importance sampling. Various models with good representation abilities have been developed but only a few of them have their importance sampling procedure. In this paper, we propose a method which provides a good bidirectional reflectance distribution function (BRDF) representation and efficient importance sampling procedure. Our method is based on representing BRDF as a function of tensor products. Four‐dimensional measured BRDF tensor data are factorized using Tucker decomposition. A large data set is used for comparing the proposed BRDF model with a number of well‐known BRDF models. It is shown that the underlying model provides good approximation to BRDFs.     

Depth of Field Effects for Interactive Direct Volume Rendering

In this paper, a method for interactive direct volume rendering is proposed for computing depth of field effects, which previously were shown to aid observers in depth and size perception of synthetically generated images. The presented technique extends those benefits to volume rendering visualizations of 3D scalar fields from CT/MRI scanners or numerical simulations. It is based on incremental filtering and as such does not depend on any pre‐computation, thus allowing interactive explorations of volumetric data sets via on‐the‐fly editing of the shading model parameters or (multi‐dimensional) transfer functions.     

Noiseless GPU rendering of isotropic BRDF surfaces

Illumination at a surface point is formulated as an integral of a BRDF using the incident radiance over the hemisphere domain. A popular method to compute the integral is Monte Carlo integration, in which the surface illumination is computed as the sum of the integrand evaluated with stochastically sampled rays. Although its simple nature is practically attractive, it incurs the serious drawback of noise artifacts due to estimator variance. In this paper, we propose a novel noiseless Monte Carlo rendering algorithm running in real time on a GPU. The main contribution is a novel importance sampling scheme, which constructs spatially continuous sample rays over a surface. For each evenly spaced polar angle of the eye ray, denoted by θ, incident rays are sampled with a PDF (probability density function) derived from a target BRDF lobe. We develop a force-based update method to create a sequence of consistent ray sets along θ’s. Finally, corresponding rays in the sequence of ray sets are linearly connected to form a continuous ray curve, referred to as a sample thread. When rendering, illumination at a surface point is computed with rays, each of which is given as a point on a sample thread. Because a thread provides a sample ray that continuously varies on a surface, the random variance of the illumination, causing visual noise during the Monte Carlo rendering process, is eliminated. A thread set is precomputed for each BRDF to free the GPU from the burden of sampling during real-time rendering. According to extensive experiments, approximately 100 threads are sufficient for most measured BRDFs with acceptable rendering quality for interactive applications.     

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.     

Shadowing Dynamic Scenes with Arbitrary BRDFs

We present a real-time relighting and shadowing method for dynamic scenes with varying lighting, view and BRDFs. Our approach is based on a compact representation of reflectance data that allows for changing the BRDF at run-time and a data-driven method for accurately synthesizing self-shadows on articulated and deformable geometries. Unlike previous self-shadowing approaches, we do not rely on local blocking heuristics. We do not fit a model to the BRDF-weighted visibility, but rather only to the visibility that changes during animation. In this manner, our model is more compact than previous techniques and requires less computation both during fitting and at run-time. Our reflectance product operators can re-integrate arbitrary low-frequency view-dependent BRDF effects on-the-fly and are compatible with all previous dynamic visibility generation techniques as well as our own data-driven visibility model. We apply our reflectance product operators to three different visibility generation models, and our data-driven model can achieve framerates well over 300Hz.     

基于Harr 小波的动态场景全频阴影绘制算法

针对现有的预计算辐射传递算法对三维场景限制严格、适合于低频光照环境等问题,提出了一种动态场景的全频阴影绘制算法.在预处理阶段使用球体对三维物体进行拟合,同时对光照函数和BRDF(bidirectional reflectance distribution function)函数进行Harr小波变换;在运行时阶段利用不同基函数的优势,在像素基空间进行多个球体可见性函数的快速合并,在小波基空间进行光照函数、BRDF函数和可见性函数的三乘积分,得到最终的光照值.使用CUDA(computed unified device architecture)实现了该算法,充分利用了图形硬件的最新功能.实验结果表明,阴影绘制质量有很大的提高,可以基本达到实时绘制.     

基于BRDF 和GPU 并行计算的全局光照实时渲染

基于光线追踪,将屏幕图像像素分解为投射光线与场景对象交点面片辐射亮度和 纹理贴图的合成,每个面片的辐射亮度计算基于双向反射分布函数(BRDF)基的线性组合,并通 过图形处理器(GPU)处理核心并行绘制进行加速,最后与并行计算的纹理映射结果进行合成。 提出了一种基于BRDF 和GPU 并行计算的全局光照实时渲染算法,利用GPU 并行加速,在提 高绘制效率的前提下,实现动态交互材质的全局光照实时渲染。重点研究：对象表面对光线的 多次反射用BRDF 基的线性组合来表示,将非线性问题转换为线性问题,从而提高绘制效率; 利用GPU 并行加速,分别计算对象表面光辐射能量和纹理映射及其线性组合,进一步提高计算 效率满足实时绘制需求。