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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 ..."
Abstract

Cited by 339 (19 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...
Survey Of Texture Mapping
 IEEE Computer Graphics and Applications
, 1986
"... This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 5667. An earlier version of thi aper appeared in Graphics Interface '86, May 1986, pp. 207212. This postscript version is missing all of the pasteup  ..."
Abstract

Cited by 182 (3 self)
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This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 5667. An earlier version of thi aper appeared in Graphics Interface '86, May 1986, pp. 207212. This postscript version is missing all of the pasteup 
Voxel space automata: modeling with stochastic growth processes in voxel space
 Computer Graphics
, 1989
"... A novel stochastic modeling technique is described which operates on a voxel data base in which objects are represented as collections of voxel records. Models are "grown " from predefined geometric elements according to rules based on simple relationships like intersection, proximity, and ..."
Abstract

Cited by 56 (0 self)
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A novel stochastic modeling technique is described which operates on a voxel data base in which objects are represented as collections of voxel records. Models are "grown " from predefined geometric elements according to rules based on simple relationships like intersection, proximity, and occlusion which can be evaluated more quickly and easily in voxel space than with analytic geometry. Growth is probabilistic: multiple trials are attempted in which an element's position and orientation are randomly perturbed, and the trial which best fits a set of rules is selected. The term voxel space automata is introduced to describe growth processes that sense and react to a voxel environment. Applications include simulation of plant growth, for which voxel representation facilitates sensing the environment. Illumination can be effidently estimated at each plant "node " at each growth iteration by casting rays into the voxel environment, allowing accurate simulation of reaction to light including heliotropism.
A Generalized Surface Appearance Representation for Computer Graphics
 University of North Carolina at Chapel
"... Computer Graphics (Under the direction of Anselmo Lastra) 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 fu ..."
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Cited by 14 (0 self)
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Computer Graphics (Under the direction of Anselmo Lastra) 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. iii To Tiffany, who has worked harder and sacrificed more for this than have I.