The Bidirectional Reflectance Distribution Function (BRDF) describes the appearance of a material by its interaction with light at a surface point. A variety of analytical models have been proposed to represent BRDFs. However, analysis of these models has been scarce due to the lack of high-resolution measured data. In this work we evaluate several well-known analytical models in terms of their ability to fit measured BRDFs. We use an existing high-resolution data set of a hundred isotropic materials and compute the best approximation for each analytical model. Furthermore, we have built a new setup for efficient acquisition of anisotropic BRDFs, which allows us to acquire anisotropic materials at high resolution. We have measured four samples of anisotropic materials (brushed aluminum, velvet, and two satins). Based on the numerical errors, function plots, and rendered images we provide insights into the performance of the various models. We conclude that for most isotropic materials physically-based analytic reflectance models can represent their appearance quite well. We illustrate the important difference between the two common ways of defining the specular lobe: around the mirror direction and with respect to the half-vector. Our evaluation shows that the latter gives a more accurate shape for the reflection lobe. Our analysis of anisotropic materials indicates current parametric reflectance models cannot represent their appearances faithfully in many cases. We show that using a sampled microfacet distribution computed from measurements improves the fit and qualitatively reproduces the measurements.

High-quality Monte Carlo image synthesis requires the ability to importance sample realistic BRDF models. However, analytic sampling algorithms exist only for the Phong model and its derivatives such as Lafortune and Blinn-Phong. This paper demonstrates an importance sampling technique for a wide range of BRDFs, including complex analytic models such as Cook-Torrance and measured materials, which are being increasingly used for realistic image synthesis. Our approach is based on a compact factored representation of the BRDF that is optimized for sampling. We show that our algorithm consistently offers better efficiency than alternatives that involve fitting and sampling a Lafortune or Blinn-Phong lobe, and is more compact than sampling strategies based on tabulating the full BRDF. We are able to efficiently create images involving multiple measured and analytic BRDFs, under both complex direct lighting and global illumination.

This paper introduces a tensor framework for image-based rendering. In particular, we develop an algorithm called TensorTextures that learns a parsimonious model of the bidirectional texture function (BTF) from observational data. Given an ensemble of images of a textured surface, our nonlinear, generative model explicitly represents the multifactor interaction implicit in the detailed appearance of the surface under varying photometric angles, including local (per-texel) reflectance, complex mesostructural self-occlusion, interreflection and self-shadowing, and other BTF-relevant phenomena. Mathematically, TensorTextures is based on multilinear algebra, the algebra of higher-order tensors, hence its name. It is computed through a decomposition known as the N-mode SVD, an extension to tensors of the conventional matrix singular value decomposition (SVD). We demonstrate the application of TensorTextures to the image-based rendering of natural and synthetic textured surfaces under continuously varying viewpoint and illumination conditions.

We consider real-time rendering of scenes in participating media, capturing the effects of light scattering in fog, mist and haze. While a number of sophisticated approaches based on Monte Carlo and finite element simulation have been developed, those methods do not work at interactive rates. The most common real-time methods are essentially simple variants of the OpenGL fog model. While easy to use and specify, that model excludes many important qualitative effects like glows around light sources, the impact of volumetric scattering on the appearance of surfaces such as the diffusing of glossy highlights, and the appearance under complex lighting such as environment maps. In this paper, we present an alternative physically based approach that captures these effects while maintaining realtime performance and the ease-of-use of the OpenGL fog model. Our method is based on an explicit analytic integration of the single scattering light transport equations for an isotropic point light source in a homogeneous participating medium. We can implement the model in modern programmable graphics hardware using a few small numerical lookup tables stored as texture maps. Our model can also be easily adapted to generate the appearances of materials with arbitrary BRDFs, environment map lighting, and precomputed radiance transfer methods, in the presence of participating media. Hence, our techniques can be widely used in real-time rendering. 1

Current systems for editing BRDFs typically allow users to adjust analytic parameters while visualizing the results in a simplified setting (e.g. unshadowed point light). This paper describes a realtime rendering system that enables interactive edits of BRDFs, as rendered in their final placement on objects in a static scene, lit by direct, complex illumination. All-frequency effects (ranging from near-mirror reflections and hard shadows to diffuse shading and soft shadows) are rendered using a precomputation-based approach. Inspired by real-time relighting methods, we create a linear system that fixes lighting and view to allow real-time BRDF manipulation. In order to linearize the image’s response to BRDF parameters, we develop an intermediate curve-based representation, which also reduces the rendering and precomputation operations to 1D while maintaining accuracy for a very general class of BRDFs. Our system can be used to edit complex analytic BRDFs (including anisotropic models), as well as measured reflectance data. We improve on the standard precomputed radiance transfer (PRT) rendering computation by introducing an incremental rendering algorithm that takes advantage of frame-to-frame coherence. We show that it is possible to render reference-quality images while only updating 10 % of the data at each frame, sustaining frame-rates of 25-30fps.

In this paper we present two novel reflectance measurement procedures that require fewer total measurements than standard uniform sampling approaches. First, we acquire densely sampled reflectance data for a large collection of different materials. Using these densely sampled measurements we analyze the general surface reflectance function to determine the local signal variation at each point in the function’s domain. We then use wavelet analysis to derive a common basis for all of the acquired reflectance functions as well as a corresponding non-uniform sampling pattern that corresponds to all non-zero wavelet coefficients. Second, we show that the reflectance of an arbitrary material can be represented as a linear combination of the surface reflectance functions. Furthermore, our analysis provides a reduced set of sampling points that permits us to robustly estimate the coefficients of this linear combination. These procedures dramatically shorten the acquisition time for isotropic reflectance measurements. We present a detailed description and analysis of our measurement approaches and sampling strategies.

Abstract—By means of passive optical motion capture, real people can be authentically animated and photo-realistically textured. To import real-world characters into virtual environments, however, surface reflectance properties must also be known. We describe a video-based modeling approach that captures human shape and motion as well as reflectance characteristics from a handful of synchronized video recordings. The presented method is able to recover spatially varying surface reflectance properties of clothes from multiview video footage. The resulting model description enables us to realistically reproduce the appearance of animated virtual actors under different lighting conditions, as well as to interchange surface attributes among different people, e.g., for virtual dressing. Our contribution can be used to create 3D renditions of real-world people under arbitrary novel lighting conditions on standard graphics hardware. Index Terms—3D video, dynamic reflectometry, real-time rendering, relighting. Ç 1

Filtering is critical for representing detail, such as color textures or normal maps, across a variety of scales. While MIP-mapping texture maps is commonplace, accurate normal map filtering remains a challenging problem because of nonlinearities in shading—we cannot simply average nearby surface normals. In this paper, we show analytically that normal map filtering can be formalized as a spherical convolution of the normal distribution function (NDF) and the BRDF, for a large class of common BRDFs such as Lambertian, microfacet and factored measurements. This theoretical result explains many previous filtering techniques as special cases, and leads to a generalization to a broader class of measured and analytic BRDFs. Our practical algorithms leverage a significant body of work that has studied lighting-BRDF convolution. We show how spherical harmonics can be used to filter the NDF for Lambertian and low-frequency specular BRDFs, while spherical von Mises-Fisher distributions can be used for high-frequency materials. 1

Tensor approximation is necessary to obtain compact multilinear models for multi-dimensional visual datasets. Traditionally, each multi-dimensional data item is represented as a vector. Such a scheme flattens the data and partially destroys the internal structures established throughout the multiple dimensions. In this paper, we retain the original dimensionality of the data items to more effectively exploit existing spatial redundancy and allow more efficient computation. Since the size of visual datasets can easily exceed the memory capacity of a single machine, we also present an outof-core algorithm for higher-order tensor approximation. The basic idea is to partition a tensor into smaller blocks and perform tensorrelated operations blockwise. We have successfully applied our techniques to three graphics-related data-driven models, including 6D bidirectional texture functions, 7D dynamic BTFs and 4D volume simulation sequences. Experimental results indicate that our techniques can not only process out-of-core data, but also achieve higher compression ratios and quality than previous methods.

of the 3D gradient field tomographically reconstructed from 16 cameras. Far right: volume rendering of the final refractive index field after