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37
NonLinear Approximation of Reflectance Functions
, 1997
"... We introduce a new class of primitive functions with nonlinear parameters for representing light reflectance functions. The functions are reciprocal, energyconserving and expressive. They can capture important phenomena such as offspecular reflection, increasing reflectance and retroreflection. ..."
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Cited by 261 (10 self)
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We introduce a new class of primitive functions with nonlinear parameters for representing light reflectance functions. The functions are reciprocal, energyconserving and expressive. They can capture important phenomena such as offspecular reflection, increasing reflectance and retroreflection. We demonstrate this by fitting sums of primitive functions to a physicallybased model and to actual measurements. The resulting representation is simple, compact and uniform. It can be applied efficiently in analytical and Monte Carlo computations. CR Categories: I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation Keywords: Reflectance function, BRDF representation 1 INTRODUCTION The bidirectional reflectance distribution function (BRDF) of a material describes how light is scattered at its surface. It determines the appearance of objects in a scene, through direct illumination and global interreflection effects. Local r...
Interactive Rendering with Arbitrary BRDFs using Separable Approximations
 IN EUROGRAPHICS RENDERING WORKSHOP
, 1999
"... A separable decomposition of bidirectional reflectance distributions (BRDFs) is used to implement arbitrary reflectances from point sources on existing graphics hardware. Twodimensional texture mapping and compositing operations are used to reconstruct samples of the BRDF at every pixel at interact ..."
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Cited by 136 (21 self)
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A separable decomposition of bidirectional reflectance distributions (BRDFs) is used to implement arbitrary reflectances from point sources on existing graphics hardware. Twodimensional texture mapping and compositing operations are used to reconstruct samples of the BRDF at every pixel at interactive rates. A change of variables, the GramSchmidt halfangle/difference vector parameterization, improves separability. Two decomposition algorithms are also presented. The singular value decomposition (SVD) minimizes RMS error. The normalized decomposition is fast and simple, using no more space than what is required for the final representation.
Homomorphic factorization of brdfs for highperformance rendering
, 2001
"... Figure 1: A model rendered at realtime rates (approximately half the performance of the standard pervertex lighting model on an NVIDIA GeForce 3) with several BRDFs approximated using the technique in this paper. From left to right: satin (anisotropic PoulinFournier model), krylon blue, garnet re ..."
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Cited by 102 (7 self)
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Figure 1: A model rendered at realtime rates (approximately half the performance of the standard pervertex lighting model on an NVIDIA GeForce 3) with several BRDFs approximated using the technique in this paper. From left to right: satin (anisotropic PoulinFournier model), krylon blue, garnet red, cayman, mystique (Cornell measured data), leather, and velvet (CURET measured data). A bidirectional reflectance distribution function (BRDF) describes how a material reflects light from its surface. To use arbitrary BRDFs in realtime rendering, a compression technique must be used to represent BRDFs using the available texturemapping and computational capabilities of an accelerated graphics pipeline. We present a numerical technique, homomorphic factorization, that can decompose arbitrary BRDFs into products of two or more factors of lower dimensionality, each factor dependent on a different interpolated geometric parameter. Compared to an earlier factorization technique based on the singular value decomposition, this new technique generates a factorization with only positive factors (which makes it more suitable for current graphics hardware accelerators), provides control over the smoothness of the result, minimizes relative rather than absolute error, and can deal with scattered, sparse data without a separate resampling and interpolation algorithm.
Interactive Rendering with Bidirectional Texture Functions
 Computer Graphics Forum
, 2003
"... We propose a new technique for efficiently rendering bidirectional texture functions (BTFs). A 6D BTF describes the appearance of a material as a texture that depends on the lighting and viewing directions. As such, a BTF accommodates selfshadowing, interreflection, and masking effects of a compl ..."
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Cited by 35 (0 self)
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We propose a new technique for efficiently rendering bidirectional texture functions (BTFs). A 6D BTF describes the appearance of a material as a texture that depends on the lighting and viewing directions. As such, a BTF accommodates selfshadowing, interreflection, and masking effects of a complex material without needing an explicit representation of the small scale geometry. Our method represents the BTF as a set of spatially varying apparent BRDFs, that each encode the reflectance field of a single pixel in the BTF. Each apparent BRDF is decomposed into a product of three or more twodimensional positive factors using a novel factorization technique, which we call chained matrix factorization (CMF). The proposed factorization technique is fully automatic and suitable for both BRDFs and apparent BRDFs (which typically exhibit offspecular peaks and nonreciprocity).
A wavelet representation of reflectance functions
 IEEE Transactions on Visualization and Computer Graphics
, 1997
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Homomorphic Factorization of BRDFbased Lighting Computation
, 2002
"... Several techniques have been developed to approximate Bidirectional Reflectance Distribution Functions (BRDF) with acceptable quality and performance for realtime applications. The recently published Homomorphic Factorization by McCool et al. is a general approximation approach that can be used with ..."
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Cited by 27 (0 self)
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Several techniques have been developed to approximate Bidirectional Reflectance Distribution Functions (BRDF) with acceptable quality and performance for realtime applications. The recently published Homomorphic Factorization by McCool et al. is a general approximation approach that can be used with various setups and for different quality requirements.
A Practitioners' Assessment of Light Reflection Models
 In Pacific Graphics
, 1997
"... We discuss the theory and practical issues behind creating reflection models to show the difficulty of the problem. We survey the current approaches towards reflection models for computer graphics to show that even for simple surfaces, the important issues are far from settled. We briefly discuss fu ..."
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Cited by 17 (4 self)
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We discuss the theory and practical issues behind creating reflection models to show the difficulty of the problem. We survey the current approaches towards reflection models for computer graphics to show that even for simple surfaces, the important issues are far from settled. We briefly discuss future directions for research. Finally, we present a case study of a particular type of light reflection that captures some important aspects of appearance for a limited class of materials with subsurface reflection. 1 Introduction A goal of realistic image synthesis is to create images that evoke visual reactions similar to what a viewer would experience in the actual scenes, or more modestly, to create images of the scenes that might be captured by a camera or other sensor device. In either case, an accurate model of the scene is needed, describing salient aspects of shapes and materials that contribute to the final images. Typically, the material description is assumed to be the easiest p...
A Generalized Surface Appearance Representation for Computer Graphics
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL
, 2002
"... For image synthesis in computer graphics, two major approaches for representing a surface’s appearance are texture mapping, which provides spatial detail, such as wallpaper, or wood grain; and the 4D bidirectional reflectance distribution function (BRDF) which provides angular detail, telling how l ..."
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Cited by 17 (0 self)
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For image synthesis in computer graphics, two major approaches for representing a surface’s appearance are texture mapping, which provides spatial detail, such as wallpaper, or wood grain; and the 4D bidirectional reflectance distribution function (BRDF) which provides angular detail, telling how light reflects off surfaces. I combine these two modes of variation to form the 6D spatial bidirectional reflectance distribution function (SBRDF). My compact SBRDF representation simply stores BRDF coefficients at each pixel of a map. I propose SBRDFs as a surface appearance representation for computer graphics and present a complete system for their use. I acquire SBRDFs of real surfaces using a device that simultaneously measures the BRDF of every point on a material. The system has the novel ability to measure anisotropy (direction of threads, scratches, or grain) uniquely at each surface point. I fit BRDF parameters using an efficient nonlinear optimization approach specific to BRDFs. SBRDFs can be rendered using graphics hardware. My approach yields significantly more detailed, general surface appearance than existing techniques for a competitive rendering cost. I also propose an SBRDF rendering method for global illumination using prefiltered environment maps. This improves on existing prefiltered environment map techniques by decoupling the BRDF from the environment maps, so a single set of maps may be used to illuminate the unique BRDFs at each surface point. I demonstrate my results using measured surfaces including gilded wallpaper, plant leaves, upholstery fabrics, wrinkled giftwrapping paper and glossy book covers.
Allfrequency relighting of glossy objects
 ACM TRANSACTIONS ON GRAPHICS
, 2006
"... We present a technique for interactive rendering of glossy objects in complex and dynamic lighting environments that captures interreflections and allfrequency shadows. Our system is based on precomputed radiance transfer and separable BRDF approximation. We factor glossy BRDFs using a separable de ..."
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Cited by 16 (2 self)
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We present a technique for interactive rendering of glossy objects in complex and dynamic lighting environments that captures interreflections and allfrequency shadows. Our system is based on precomputed radiance transfer and separable BRDF approximation. We factor glossy BRDFs using a separable decomposition and keep only a few loworder approximation terms, each consisting of a purely viewdependent and a purely lightdependent component. In the precomputation step, for every vertex we sample its visibility and compute a direct illumination transport vector corresponding to each BRDF term. We use modern graphics hardware to accelerate this step, and further compress the data using a nonlinear wavelet approximation. The direct illumination pass is followed by one or more interreflection passes, each of which gathers compressed transport vectors from the previous pass to produce global illumination transport vectors. To render at run time, we dynamically sample the lighting to produce a light vector, also represented in a wavelet basis. We compute the inner product of the light vector with the precomputed transport vectors, and the results are further combined with the BRDF viewdependent components to produce vertex colors. We describe acceleration of the rendering algorithm using programmable graphics hardware, and discuss the limitations and tradeoffs imposed by the hardware.