We present a generative model for isotropic bidirectional reflectance distribution functions (BRDFs) based on acquired reflectance data. Instead of using analytical reflectance models, we represent each BRDF as a dense set of measurements. This allows us to interpolate and extrapolate in the space of acquired BRDFs to create new BRDFs. We treat each acquired BRDF as a single high-dimensional vector taken from a space of all possible BRDFs. We apply both linear (subspace) and non-linear (manifold) dimensionality reduction tools in an effort to discover a lowerdimensional representation that characterizes our measurements. We let users define perceptually meaningful parametrization directions to navigate in the reduced-dimension BRDF space. On the low-dimensional manifold, movement along these directions produces novel but valid BRDFs.

graphics hardware, illumination, image processing, image-based rendering, reflectance & shading models, texture mapping In this paper we present a new form of texture mapping that produces increased photorealism. Coefficients of a biquadratic polynomial are stored per texel, and used to reconstruct the surface color under varying lighting conditions. Like bump mapping, this allows the perception of surface deformations. However, our method is image based, and photographs of a surface under varying lighting conditions can be used to construct these maps. Unlike bump maps, these Polynomial Texture Maps (PTMs) also capture variations due to surface self-shadowing and interreflections, which enhance realism. Surface colors can be efficiently reconstructed from polynomial coefficients and light directions with minimal fixed-point hardware. We have also found PTMs useful for producing a number of other effects such as anisotropic and Fresnel shading models and variable depth of focus. Lastly, we present several reflectance function transformations that act as contrast enhancement operators. We have found these particularly useful in the study of ancient archeological clay and stone writings.

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Figure 1: These images, showing many different lighting conditions and BRDFs, were each rendered at approximately 30 frames per second using our Spherical Harmonic Reflection Map (SHRM) representation. From left to right, a simplified microfacet BRDF, krylon blue (using McCool et al.’s reconstruction from measurements at Cornell), orange and velvet (CURET database), and an anisotropic BRDF (based on the Kajiya-Kay model). The environment maps are the Grace Cathedral, St. Peter’s Basilica, the Uffizi gallery, and a Eucalyptus grove, courtesy Paul Debevec. The armadillo model is from Venkat Krishnamurthy. We present a new method for real-time rendering of objects with complex isotropic BRDFs under distant natural illumination, as specified by an environment map. Our approach is based on spherical frequency space analysis and includes three main contributions. Firstly, we are able to theoretically analyze required sampling rates and resolutions, which have traditionally been determined in an ad-hoc manner. We also introduce a new compact representation, which we call a spherical harmonic reflection map (SHRM), for efficient representation and rendering. Finally, we show how to rapidly prefilter the environment map to compute the SHRM—our frequency domain prefiltering algorithm is generally orders of magnitude faster than previous angular (spatial) domain approaches.

a) b) c) d) e) f) Figure 1 From a) photographs of an object taken under varying illumination (one of ten photographs is shown here), we reconstruct b) its normals and materials, represented as c) a material weight map controlling a mixture of d,e) fundamental materials. Using this representation we can f) re-render the object under novel lighting. This paper describes a photometric stereo method designed for surfaces with spatially-varying BRDFs, including sur-faces with both varying diffuse and specular properties. Our method builds on the observation that most objects are composed of a small number of fundamental materials. This approach recovers not only the shape but also material BRDFs and weight maps, yielding compelling results for a wide variety of objects. We also show examples of interac-tive lighting and editing operations made possible by our method. 1

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.

A method is presented that takes as an input a 2D microfacet orientation distribution and produces a 4D bidirectional reflectance distribution function (BRDF). This method differs from previous microfacet-based BRDF models in that it uses a simple shadowing term which allows it to handle very general microfacet distributions while maintaining reciprocity and energy conservation. The generator is shown on a variety of material types.

. The measurement of accurate material properties is an important step towards photorealistic rendering. Many real-world objects are composed of a number of materials that often show subtle changes even within a single material. Thus, for photorealistic rendering both the general surface properties as well as the spatially varying effects of the object are needed. We present an image-based measuring method that robustly detects the different materials of real objects and fits an average bidirectional reflectance distribution function (BRDF) to each of them. In order to model the local changes as well, we project the measured data for each surface point into a basis formed by the recovered BRDFs leading to a truly spatially varying BRDF representation. A high quality model of a real object can be generated with relatively few input data. The generated model allows for rendering under arbitrary viewing and lighting conditions and realistically reproduces the appearance of the original object. 1

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.