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88
Lambertian Reflectance and Linear Subspaces
, 2000
"... We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wi ..."
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Cited by 336 (21 self)
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We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a lowdimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. Finally, we show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. Research conducted w...
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...
RENDERING FUR WITH THREE DIMENSIONAL TEXTURES
, 1989
"... We present a method for rendering scenes with fine detail via an object called a texel, a rendering primitive inspired by volume densities mixed with anisotropic lighting models. This technique solves a long outstanding problem in image synthesis: the rendering of furry surfaces. ..."
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Cited by 210 (0 self)
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We present a method for rendering scenes with fine detail via an object called a texel, a rendering primitive inspired by volume densities mixed with anisotropic lighting models. This technique solves a long outstanding problem in image synthesis: the rendering of furry surfaces.
A SignalProcessing Framework for Inverse Rendering
 In SIGGRAPH 01
, 2001
"... Realism in computergenerated images requires accurate input models for lighting, textures and BRDFs. One of the best ways of obtaining highquality data is through measurements of scene attributes from real photographs by inverse rendering. However, inverse rendering methods have been largely limit ..."
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Cited by 186 (18 self)
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Realism in computergenerated images requires accurate input models for lighting, textures and BRDFs. One of the best ways of obtaining highquality data is through measurements of scene attributes from real photographs by inverse rendering. However, inverse rendering methods have been largely limited to settings with highly controlled lighting. One of the reasons for this is the lack of a coherent mathematical framework for inverse rendering under general illumination conditions. Our main contribution is the introduction of a signalprocessing framework which describes the reflected light field as a convolution of the lighting and BRDF, and expresses it mathematically as a product of spherical harmonic coefficients of the BRDF and the lighting. Inverse rendering can then be viewed as deconvolution. We apply this theory to a variety of problems in inverse rendering, explaining a number of previous empirical results. We will show why certain problems are illposed or numerically illconditioned, and why other problems are more amenable to solution. The theory developed here also leads to new practical representations and algorithms. For instance, we present a method to factor the lighting and BRDF from a small number of views, i.e. to estimate both simultaneously when neither is known.
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
An Efficient Representation for Irradiance Environment Maps
, 2001
"... We consider the rendering of diffuse objects under distant illumination, as specified by an environment map. Using an analytic expression for the irradiance in terms of spherical harmonic coefficients of the lighting, we show that one needs to compute and use only 9 coefficients, corresponding to th ..."
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Cited by 158 (10 self)
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We consider the rendering of diffuse objects under distant illumination, as specified by an environment map. Using an analytic expression for the irradiance in terms of spherical harmonic coefficients of the lighting, we show that one needs to compute and use only 9 coefficients, corresponding to the lowestfrequency modes of the illumination, in order to achieve average errors of only 1%. In other words, the irradiance is insensitive to high frequencies in the lighting, and is well approximated using only 9 parameters. In fact, we show that the irradiance can be procedurally represented simply as a quadratic polynomial in the cartesian components of the surface normal, and give explicit formulae. These observations lead to a simple and efficient procedural rendering algorithm amenable to hardware implementation, a prefiltering method up to three orders of magnitude faster than previous techniques, and new representations for lighting design and imagebased rendering.
Displaced subdivision surfaces
 Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH
, 2000
"... In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivisio ..."
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Cited by 130 (1 self)
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In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. Additional Keywords: geometry compression, multiresolution geometry, displacement maps, bump maps, multiresolution editing, animation.
Polynomial texture maps
 In Computer Graphics, SIGGRAPH 2001 Proceedings
, 2001
"... graphics hardware, illumination, image processing, imagebased 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 ..."
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Cited by 128 (8 self)
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graphics hardware, illumination, image processing, imagebased 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 selfshadowing and interreflections, which enhance realism. Surface colors can be efficiently reconstructed from polynomial coefficients and light directions with minimal fixedpoint 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.
On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object
, 2001
"... This paper presents a theoretical analysis of the relationship between incoming radiance and irradiance. Radiance and irradiance are basic optical quantities, and their relationship is of fundamental interest to many fields, including computer vision, radiative transfer, and computer graphics. Physi ..."
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Cited by 116 (10 self)
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This paper presents a theoretical analysis of the relationship between incoming radiance and irradiance. Radiance and irradiance are basic optical quantities, and their relationship is of fundamental interest to many fields, including computer vision, radiative transfer, and computer graphics. Physically, we are interested in analyzing the properties of the light field generated when a homogeneous convex curved Lambertian surface of known geometry reflects a distant illumination field. A Lambertian surface reflects light proportional to the incoming irradiance, so analysis of this physical system is equivalent to a mathematical analysis of the relationship between incoming radiance and irradiance
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.