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.     

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.     

Estimating Specular Roughness and Anisotropy from Second Order Spherical Gradient Illumination

This paper presents a novel method for estimating specular roughness and tangent vectors, per surface point, from polarized second order spherical gradient illumination patterns. We demonstrate that for isotropic BRDFs, only three second order spherical gradients are sufficient to robustly estimate spatially varying specular roughness. For anisotropic BRDFs, an additional two measurements yield specular roughness and tangent vectors per surface point. We verify our approach with different illumination configurations which project both discrete and continuous fields of gradient illumination. Our technique provides a direct estimate of the per-pixel specular roughness and thus does not require off-line numerical optimization that is typical for the measure-and-fit approach to classical BRDF modeling.     

A PCA Decomposition for Real‐time BRDF Editing and Relighting with Global Illumination

We propose a novel rendering method which supports interactive BRDF editing as well as relighting on a 3D scene. For interactive BRDF editing, we linearize an analytic BRDF model with basis BRDFs obtained from a principal component analysis. For each basis BRDF, the radiance transfer is precomputed and stored in vector form. In rendering time, illumination of a point is computed by multiplying the radiance transfer vectors of the basis BRDFs by the incoming radiance from gather samples and then linearly combining the results weighted by user‐controlled parameters. To improve the level of accuracy, a set of sub‐area samples associated with a gather sample refines the glossy reflection of the geometric details without increasing the precomputation time. We demonstrate this program with a number of examples to verify the real‐time performance of relighting and BRDF editing on 3D scenes with complex lighting and geometry.     

Spectralization: Reconstructing spectra from sparse data

Traditional RGB reflectance and light data suffers from the problem of metamerism and is not suitable for rendering purposes where exact color reproduction under many different lighting conditions is needed. Nowadays many setups for cheap and fast acquisition of RGB or similar trichromatic datasets are available. In contrast to this, multi‐ or even hyper‐spectral measurements require costly hardware and have severe limitations in many cases. In this paper, we present an approach to combine efficiently captured RGB data with spectral data that can be captured with small additional effort for example by scanning a single line of an image using a spectral line‐scanner. Our algorithm can infer spectral reflectances and illumination from such sparse spectral and dense RGB data. Unlike other approaches, our method reaches acceptable perceptual errors with only three channels for the dense data and thus enables further use of highly efficient RGB capture systems. This way, we are able to provide an easier and cheaper way to capture spectral textures, BRDFs and environment maps for the use in spectral rendering systems.     

A Resolution Independent Approach for the Accurate Rendering of Grooved Surfaces

This paper presents a method for the accurate rendering of path‐based surface details such as grooves, scratches and similar features. The method is based on a continuous representation of the features in texture space, and the rendering is performed by means of two approaches: one for isolated or non‐intersecting grooves and another for special situations like intersections or ends. The proposed solutions perform correct antialiasing and take into account visibility and inter‐reflections with little computational effort and memory requirements. Compared to anisotropic BRDFs and scratch models, we have no limitations on the distribution of grooves over the surface or their geometry, thus allowing more general patterns. Compared to displacement mapping techniques, we can efficiently simulate features of all sizes without requiring additional geometry or multiple representations.     

Accurate fitting of measured reflectances using a Shifted Gamma micro‐facet distribution

Material models are essential to the production of photo‐realistic images. Measured BRDFs provide accurate representation with complex visual appearance, but have larger storage cost. Analytical BRDFs such as Cook‐Torrance provide a compact representation but fail to represent the effects we observe with measured appearance. Accurately fitting an analytical BRDF to measured data remains a challenging problem. In this paper we introduce the SGD micro‐facet distribution for Cook‐Torrance BRDF. This distribution accurately models the behavior of most materials. As a consequence, we accurately represent all measured BRDFs using a single lobe. Our fitting procedure is stable and robust, and does not require manual tweaking of the parameters.     

Analytic Tangent Irradiance Environment Maps for Anisotropic Surfaces

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

Interactive 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.     

An Error Estimation Framework for Many‐Light Rendering

The popularity of many‐light rendering, which converts complex global illumination computations into a simple sum of the illumination from virtual point lights (VPLs), for predictive rendering has increased in recent years. A huge number of VPLs are usually required for predictive rendering at the cost of extensive computational time. While previous methods can achieve significant speedup by clustering VPLs, none of these previous methods can estimate the total errors due to clustering. This drawback imposes on users tedious trial and error processes to obtain rendered images with reliable accuracy. In this paper, we propose an error estimation framework for many‐light rendering. Our method transforms VPL clustering into stratified sampling combined with confidence intervals, which enables the user to estimate the error due to clustering without the costly computing required to sum the illumination from all the VPLs. Our estimation framework is capable of handling arbitrary BRDFs and is accelerated by using visibility caching, both of which make our method more practical. The experimental results demonstrate that our method can estimate the error much more accurately than the previous clustering method.     

Wetting Effects in Hair Simulation

There is considerable recent progress in hair simulations, driven by the high demands in computer animated movies. However, capturing the complex interactions between hair and water is still relatively in its infancy. Such interactions are best modeled as those between water and an anisotropic permeable medium as water can flow into and out of the hair volume biased in hair fiber direction. Modeling the interaction is further challenged when the hair is allowed to move. In this paper, we introduce a simulation model that reproduces interactions between water and hair as a dynamic anisotropic permeable material. We utilize an Eulerian approach for capturing the microscopic porosity of hair and handle the wetting effects using a Cartesian bounding grid. A Lagrangian approach is used to simulate every single hair strand including interactions with each other, yielding fine‐detailed dynamic hair simulation. Our model and simulation generate many interesting effects of interactions between fine‐detailed dynamic hair and water, i.e., water absorption and diffusion, cohesion of wet hair strands, water flow within the hair volume, water dripping from the wet hair strands and morphological shape transformations of wet hair.     

Approximate on‐Surface Distance Computation using Quasi‐Developable Charts

There is a vast number of applications that require distance field computation over triangular meshes. State‐of‐the‐art algorithms have quadratic or sub‐quadratic worst‐case complexity, making them impractical for interactive applications. While most of the research on this subject has been focused on reducing the computation complexity of the algorithms, in this work we propose an approximate algorithm that achieves similar results working in lower resolutions of the input meshes. The creation of lower resolution meshes is the essence of our proposal. The idea is to identify regions on the input mesh that can be unfolded into planar regions with minimal area distortion (i.e. quasi‐developable charts). Once charts are computed, their interior is re‐triangulated to reduce the number of triangles, which results in a collection of simplified charts that we call a base mesh. Due to the properties of quasi‐developable regions, we are able to compute distance fields over the base mesh instead of over the input mesh. This reduces the memory footprint and data processed for distance computations, which is the bottleneck of these algorithms. We present results that are one order of magnitude faster than current exact solutions, with low approximation errors.     

Visibility Editing For All‐Frequency Shadow Design

We present an approach for editing shadows in all‐frequency lighting environments. To support artistic control, we propose to decouple shadowing from lighting and focus on providing intuitive controls to edit the former. To accomplish this task, we precompute and store scene visibility information separately from lighting and BRDFs and allow artists to edit visibility directly, by providing operations to select shadows and edit their shape. To facilitate a wider range of editing operations, we generalize visibility from binary to three‐channel oating point quantities and introduce a novel shadow representation based on computation of visibility ratios between the original render and the edited one. We demonstrate our results for diffuse and glossy surfaces, still scenes and animations.     

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.     

Progressive Virtual Beam Lights

A recent technique that forms virtual ray lights (VRLs) from path segments in media, reduces the artifacts common to VPL approaches in participating media, however, distracting singularities still remain. We present Virtual Beam Lights (VBLs), a progressive many‐lights algorithm for rendering complex indirect transport paths in, from, and to media. VBLs are efficient and can handle heterogeneous media, anisotropic scattering, and moderately glossy surfaces, while provably converging to ground truth. We inflate ray lights into beam lights with finite thicknesses to eliminate the remaining singularities. Furthermore, we devise several practical schemes for importance sampling the various transport contributions between camera rays, light rays, and surface points. VBLs produce artifact‐free images faster than VRLs, especially when glossy surfaces and/or anisotropic phase functions are present. Lastly, we employ a progressive thickness reduction scheme for VBLs in order to render results that converge to ground truth.     

Heightfield and spatially varying BRDF Reconstruction for Materials with Interreflections

Photo-realistic reproduction of material appearance from images has widespread use in applications ranging from movies over advertising to virtual prototyping. A common approach to this task is to reconstruct the small scale geometry of the sample and to capture the reflectance properties using spatially varying BRDFs. For this, multi-view and photometric stereo reconstruction can be used, both of which are limited regarding the amount of either view or light directions and suffer from either low- or high-frequency artifacts, respectively. In this paper, we propose a new algorithm combining both techniques to recover heightfields and spatially varying BRDFs while at the same time overcoming the above mentioned drawbacks. Our main contribution is a novel objective function which allows for the reconstruction of a heightfield and high quality SVBRDF including view dependent effects. Thereby, our method also avoids both low and high frequency artifacts. Additionally, our algorithm takes inter-reflections into account allowing for the reconstruction of undisturbed representations of the underlying material. In our experiments, including synthetic and real-world data, we show that our approach is superior to state-of-the-art methods regarding reconstruction error as well as visual impression. Both the reconstructed geometry and the recovered SVBRDF are highly accurate, resulting in a faithful reproduction of the materials characteristic appearance, which is of paramount importance in the context of material rendering.     

EnvyDepth: An Interface for Recovering Local Natural Illumination from Environment Maps

In this paper, we present EnvyDepth, an interface for recovering local illumination from a single HDR environment map. In EnvyDepth, the user quickly indicates strokes to mark regions of the environment map that should be grouped together in a single geometric primitive. From these annotated strokes, EnvyDepth uses edit propagation to create a detailed collection of virtual point lights that reproduce both the local and the distant lighting effects in the original scene. When compared to the sole use of the distant illumination, the added spatial information better reproduces a variety of local effects such as shadows, highlights and caustics. Without the effort needed to create precise scene reconstructions, EnvyDepth annotations take only tens of seconds to produce a plausible lighting without visible artifacts. This is easy to obtain even in the case of complex scenes, both indoors and outdoors. The generated lighting environments work well in a production pipeline since they are efficient to use and able to produce accurate renderings.     

Pre‐convolved Radiance Caching

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

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.