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22
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 514 (20 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...
Precomputed Radiance Transfer for RealTime Rendering in Dynamic, LowFrequency Lighting Environments
 ACM Transactions on Graphics
, 2002
"... We present a new, realtime method for rendering diffuse and glossy objects in lowfrequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of ..."
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Cited by 472 (28 self)
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We present a new, realtime method for rendering diffuse and glossy objects in lowfrequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of arbitrary, lowfrequency incident lighting into transferred radiance which includes global effects like shadows and interreflections from the object onto itself. At runtime, these transfer functions are applied to actual incident lighting. Dynamic, local lighting is handled by sampling it close to the object every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using loworder spherical harmonics. This avoids aliasing and evaluates efficiently on graphics hardware by reducing the shading integral to a dot product of 9 to 25 element vectors for diffuse receivers. Glossy objects are handled using matrices rather than vectors. We further introduce functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space. These allow soft shadows and caustics from rigidly moving objects to be cast onto arbitrary, dynamic receivers. We demonstrate realtime global lighting effects with this approach.
Allfrequency shadows using nonlinear wavelet lighting approximation
 ACM Transactions on Graphics
, 2003
"... We present a method, based on precomputed light transport, for realtime rendering of objects under allfrequency, timevarying illumination represented as a highresolution environment map. Current techniques are limited to small area lights, with sharp shadows, or large lowfrequency lights, with ..."
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Cited by 186 (25 self)
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We present a method, based on precomputed light transport, for realtime rendering of objects under allfrequency, timevarying illumination represented as a highresolution environment map. Current techniques are limited to small area lights, with sharp shadows, or large lowfrequency lights, with very soft shadows. Our main contribution is to approximate the environment map in a wavelet basis, keeping only the largest terms (this is known as a nonlinear approximation). We obtain further compression by encoding the light transport matrix sparsely but accurately in the same basis. Rendering is performed by multiplying a sparse light vector by a sparse transport matrix, which is very fast. For accurate rendering, using nonlinear wavelets is an order of magnitude faster than using linear spherical harmonics, the current best technique.
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 reconstr ..."
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Cited by 176 (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.
Inverse Rendering for Computer Graphics
, 1998
"... Creating realistic images has been a major focus in the study of computer graphics for much of its history. This effort has led to mathematical models and algorithms that can compute predictive, or physically realistic, images from known camera positions and scene descriptions that include the geome ..."
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Cited by 100 (4 self)
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Creating realistic images has been a major focus in the study of computer graphics for much of its history. This effort has led to mathematical models and algorithms that can compute predictive, or physically realistic, images from known camera positions and scene descriptions that include the geometry of objects, the reflectance of surfaces, and the lighting used to illuminate the scene. These images accurately describe the physical quantities that would be measured from a real scene. Because these algorithms can predict real images, they can also be used in inverse problems to work backward from photographs to attributes of the scene. Work on three such inverse rendering problems is described. The first, inverse lighting, assumes knowledge of geometry, reflectance, and the recorded photograph and solves for the lighting in the scene. A technique using a linear leastsquares system is proposed and demonstrated. Also demonstrated is an application of inverse lighting, called relighting, which modi es lighting in photographs. The second two inverse rendering problems solve for unknown reflectance, given images with known geometry, lighting, and camera positions. Photographic texture measurement
Determining generative models of objects under varying illumination: Shape and albedo from multiple images using svd and integrability
 International Journal of Computer Vision
, 1999
"... We describe a method of learning generative models of objects from a set of images of the object under different, and unknown, illumination. Such a model allows us to approximate the objects’ appearance under a range of lighting conditions. This work is closely related to photometric stereo with unk ..."
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Cited by 88 (3 self)
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We describe a method of learning generative models of objects from a set of images of the object under different, and unknown, illumination. Such a model allows us to approximate the objects’ appearance under a range of lighting conditions. This work is closely related to photometric stereo with unknown light sources and, in particular, to the use of Singular Value Decomposition (SVD) to estimate shape and albedo from multiple images up to a linear transformation [15]. Firstly we analyze and extend the SVD approach to this problem. We demonstrate that it applies to objects for which the dominant imaging effects are Lambertian reflectance with a distant light source and a background ambient term. To determine that this is a reasonable approximation we calculate the eigenvectors of the SVD on a set of real objects, under varying lighting conditions, and demonstrate that the first few eigenvectors account for most of the data in agreement with our predictions. We then analyze the linear ambiguities in the SVD approach and demonstrate that previous methods proposed to resolve them [15] are only valid under certain conditions. We discuss alternative possibilities and, in particular, demonstrate that knowledge of the object class is sufficient to resolve this problem. Secondly, we describe the use of surface consistency for putting constraints on the possible solutions. We prove that this constraint reduces the ambiguities to a subspace called the generalized bas relief ambiguity (GBR) which is inherent in the Lambertian reflectance function (and which can be shown to exist even if attached and cast shadows are present [3]). We demonstrate the use of surface consistency to solve for the shape and albedo up to a GBR and describe, and implement, a variety of additional assumptions to resolve the GBR. Thirdly, we demonstrate an iterative algorithm that can detect and remove some attached shadows from the objects thereby increasing the accuracy of the reconstructed shape and albedo. 1
Viewdependent precomputed light transport using nonlinear gaussian function approximations
 In ACM Symposium on Interactive 3D graphics
, 2006
"... We propose a realtime method for rendering rigid objects with complex viewdependent effects under distant allfrequency lighting. Existing precomputed light transport approaches can render rich global illumination effects, but highfrequency viewdependent effects such as sharp highlights remain a ..."
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Cited by 28 (4 self)
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We propose a realtime method for rendering rigid objects with complex viewdependent effects under distant allfrequency lighting. Existing precomputed light transport approaches can render rich global illumination effects, but highfrequency viewdependent effects such as sharp highlights remain a challenge. We introduce a new representation of the light transport operator based on sums of Gaussians. The nonlinear parameters of our representation enable 1) arbitrary bandwidth because scale is encoded as a direct parameter, and 2) highquality interpolation across view and mesh triangles because we interpolate the mean direction of the Gaussians, thereby preventing linear crossfading artifacts. However, fitting the precomputed light transport data to this new representation requires solving a nonlinear regression problem that is more involved than traditional linear and nonlinear (truncation) approximation techniques. We present a new data fitting method based on optimization that includes energy terms aimed at enforcing artifactfree interpolation. We demonstrate that our method achieves high visual quality with a small storage cost and an efficient rendering algorithm.
Lighting sensitive display
 ACM Trans. Graphics
, 2004
"... Although display devices have been used for decades, they have functioned without taking into account the illumination of their environment. We present the concept of a lighting sensitive display (LSD) – a display that measures the incident illumination and modifies its content accordingly. An idea ..."
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Cited by 23 (5 self)
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Although display devices have been used for decades, they have functioned without taking into account the illumination of their environment. We present the concept of a lighting sensitive display (LSD) – a display that measures the incident illumination and modifies its content accordingly. An ideal LSD would be able to measure the 4D illumination field incident upon it and generate a 4D light field in response to the illumination. However, current sensing and display technologies do not allow for such an ideal implementation. Our initial prototype of the LSD uses a 2D measurement of the illumination field and produces a 2D image in response to it. In particular, it renders a 3D scene such that it always appears to be lit by the real environment that the display resides in. The current system is designed to perform best when the light sources in the environment are distant from the display, and a single user in a known location views the display. The displayed scene is represented by compressing a very large set of images (acquired or rendered) of the scene that correspond to different lighting conditions. The compression algorithm is a lossy one that exploits not only image correlations over the illumination dimensions but also coherences over the spatial dimensions of the image. This results in a highly compressed
Steerable Illumination Textures
 ACM Transactions on Graphics
, 2002
"... We introduce a new set of illumination basis functions designed for lighting bumpy surfaces. This lighting includes shadowing and interreflection. To create an image with a new light direction, only a linear combination of precomputed textures is required. This is possible by using a carefully selec ..."
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Cited by 19 (0 self)
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We introduce a new set of illumination basis functions designed for lighting bumpy surfaces. This lighting includes shadowing and interreflection. To create an image with a new light direction, only a linear combination of precomputed textures is required. This is possible by using a carefully selected set of steerable basis functions. Steerable basis lights have the property that they allow lights to move continuously without jarring visual artifacts. The new basis lights are shown to produce images of high visual quality with as few as 49 basis textures.