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61
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 218 (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...
Reflection from Layered Surfaces due to Subsurface Scattering
, 1993
"... The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or microfacets. Diffuse reflection is generally considered to result from ..."
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Cited by 185 (3 self)
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The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or microfacets. Diffuse reflection is generally considered to result from multiple scattering either from a rough surface or from within a layer near the surface. Accounting for diffuse reflection by Lambert's Cosine Law, as is universally done in computer graphics, is not a physical theory based on first principles. This paper presents
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 114 (20 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.
Generalization of the Lambertian Model and Implications for Machine Vision
, 1992
"... Lambert's model for diffuse reflection is extensively used in computational vision. It is used explicitly by methods such as shape from shading and photometric stereo, and implicitly by methods such as binocular stereo and motion detection. For several realworld objects, the Lambertian model can pro ..."
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Cited by 99 (12 self)
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Lambert's model for diffuse reflection is extensively used in computational vision. It is used explicitly by methods such as shape from shading and photometric stereo, and implicitly by methods such as binocular stereo and motion detection. For several realworld objects, the Lambertian model can prove to be a very inaccurate approximation to the diffuse component. While the brightness of a Lambertian surface is independent of viewing direction, the brightness of a rough diffuse surface increases as the viewer approaches the source direction. A comprehensive model is developed that predicts reflectance from rough diffuse surfaces. The model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between points on the surface. Experiments have been conducted on real samples, such as, plaster, clay, sand, and cloth. All these surfaces demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in s...
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 85 (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.
Reflection Space Image Based Rendering
, 1999
"... High quality, physically accurate rendering at interactive rates has widespread application, but is a daunting task. We attempt to bridge the gap between highquality offline and interactive rendering by using existing environment mapping hardware in combination with a novel Image Based Rendering (I ..."
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Cited by 81 (1 self)
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High quality, physically accurate rendering at interactive rates has widespread application, but is a daunting task. We attempt to bridge the gap between highquality offline and interactive rendering by using existing environment mapping hardware in combination with a novel Image Based Rendering (IBR) algorithm. The primary contribution lies in performing IBR in reflection space. This method can be applied to ordinary environment maps, but for more physically accurate rendering, we apply reflection space IBR to radiance environment maps. A radiance environment map preintegrates a Bidirectional Reflection Distribution Function (BRDF) with a lighting environment. Using the reflectionspace IBR algorithm on radiance environment maps allows interactive rendering of arbitrary objects with a large class of complex BRDFs in arbitrary lighting environments. The ultimate simplicity of the final algorithm suggests that it will be widely and immediately valuable given the ready availability of hardware assisted environment mapping.
Generalization of Lambert's Reflectance Model
 In SIGGRAPH 94
, 1994
"... Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several realworld objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the bright ..."
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Cited by 77 (2 self)
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Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several realworld objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently nonLambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All...
A Microfacetbased BRDF Generator
, 2000
"... 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 microfacetbased BRDF models in that it uses a simple shadowing term which allows it to handle very genera ..."
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Cited by 77 (3 self)
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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 microfacetbased 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.
An Inexpensive BRDF Model for Physicallybased Rendering
, 1994
"... : A new BRDF model is presented which can be viewed as an kind of intermediary model between empirism and theory. Main results of physics are observed (energy conservation, reciprocity rule, microfacet theory) and numerous phenomena involved in light reflection are accounted for, in a physically pla ..."
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Cited by 72 (3 self)
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: A new BRDF model is presented which can be viewed as an kind of intermediary model between empirism and theory. Main results of physics are observed (energy conservation, reciprocity rule, microfacet theory) and numerous phenomena involved in light reflection are accounted for, in a physically plausible way (incoherent and coherent reflection, spectrum modifications, anisotropy, selfshadowing, multiple reflection, surface and subsurface reflection, differences between homogeneous and heterogeneous materials). The model has been especially intended for computer graphics applications and therefore includes two main features : simplicity (a small number of intuitively understandable parameters controls the model) and efficiency (the formulation insures adequation to MonteCarlo rendering techniques and/or hardware implementations). Keywords : PhysicallyBased Rendering, Bidirectional Reflectance Distribution Function, Optimization 1 Introduction Computation of a reflectance model i...
Efficient BRDF Importance Sampling Using A Factored Representation
 ACM TRANS. GRAPH
, 2004
"... Highquality 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 BlinnPhong. This paper demonstrates an importance sampling technique for a wide ra ..."
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Cited by 62 (7 self)
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Highquality 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 BlinnPhong. This paper demonstrates an importance sampling technique for a wide range of BRDFs, including complex analytic models such as CookTorrance 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 BlinnPhong 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.