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89
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 526 (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...
Deriving Intrinsic Images from Image Sequences
, 2001
"... Intrinsic images are a useful midlevel description of scenes proposed by Barrow and Tenebaum [1]. An image is decomposed into two images: a reflectance image and an illumination image. Finding such a decomposition remains a difficult problem in computer vision. Here we focus on a slightly easier pro ..."
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Cited by 253 (5 self)
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Intrinsic images are a useful midlevel description of scenes proposed by Barrow and Tenebaum [1]. An image is decomposed into two images: a reflectance image and an illumination image. Finding such a decomposition remains a difficult problem in computer vision. Here we focus on a slightly easier problem: given a sequence of T images where the reflectance is constant and the illumination changes, can we recover T illumination images and a single reflectance image? We show that this problem is still illposed and suggest approaching it as a maximumlikelihood estimation problem. Following recent work on the statistics of natural images, we use a prior that assumes that illumination images will give rise to sparse filter outputs. We show that this leads to a simple, novel algorithm for recovering reflectance images. We illustrate the algorithm's performance on real and synthetic image sequences.
A Framework for Robust Subspace Learning
 International Journal of Computer Vision
, 2003
"... Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications. ..."
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Cited by 177 (10 self)
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Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications.
Photometric Stereo with General, Unknown Lighting
 In IEEE Conference on Computer Vision and Pattern Recognition
, 2001
"... Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on the presence of a single point source of light in each image. In this paper we ..."
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Cited by 138 (8 self)
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Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on the presence of a single point source of light in each image. In this paper we show how to perform photometric stereo assuming that all lights in a scene are isotropic and distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and arbitrary combination of diffuse, point and extended sources. Our work is based on recent results showing that for Lambertian objects, general lighting conditions can be represented using low order spherical harmonics. Using this representation we can recover shape by performing a simple optimization in a lowdimensional space. We also analyze the shape ambiguities that arise in such a representation. 1.
Analytic PCA Construction for Theoretical Analysis of Lighting Variability in Images of a Lambertian Object
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2002
"... Lambertian object ..."
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Joint Manifold Distance: a new approach to appearance based clustering,”
 IEEE Conference on Computer Vision and Pattern Recognition (CVPR ’03) 
, 2003
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Tales of Shape and Radiance in Multiview Stereo
, 2002
"... To what extent can threedimensional shape and radiance be inferred from a collection of images? Can the two be estimated separately while retaining optimality? How should the optimality criterion be computed? When is it necessary to employ an explicit model of the reflectance properties of a scene? ..."
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Cited by 44 (10 self)
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To what extent can threedimensional shape and radiance be inferred from a collection of images? Can the two be estimated separately while retaining optimality? How should the optimality criterion be computed? When is it necessary to employ an explicit model of the reflectance properties of a scene? In this paper we introduce a separation principle for shape and radiance estimation that applies to Lambertian scenes and holds for any choice of norm. When the scene is not Lambertian, however, shape cannot be decoupled from radiance, and therefore matching imagetoimage is not possible directly. We employ a rank constraint on the radiance tensor, which is commonly used in computer graphics, and construct a novel cost functional whose minimization leads to an estimate of both shape and radiance for nonLambertian objects, which we validate experimentally. 1
Shedding light on stereoscopic segmentation
 In CVPR
, 2004
"... We propose a variational algorithm to jointly estimate the shape, albedo, and light configuration of a Lambertian scene from a collection of images taken from different vantage points. Our work can be thought of as extending classical multiview stereo to cases where point correspondence cannot be e ..."
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Cited by 33 (3 self)
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We propose a variational algorithm to jointly estimate the shape, albedo, and light configuration of a Lambertian scene from a collection of images taken from different vantage points. Our work can be thought of as extending classical multiview stereo to cases where point correspondence cannot be established, or extending classical shape from shading to the case of multiple views with unknown light sources. We show that a first naive formalization of this problem yields algorithms that are numerically unstable, no matter how close the initialization is to the true geometry. We then propose a computational scheme to overcome this problem, resulting in provably stable algorithms that converge to (local) minima of the cost functional. Although we restrict our attention to Lambertian objects with uniform albedo, extensions of our framework are conceivable. 1
Selfcalibrating photometric stereo
 IN: PROC. IEEE CONF. COMPUTER VISION AND PATTERN RECOGNITION
, 2010
"... We present a selfcalibrating photometric stereo method. From a set of images taken from a fixed viewpoint under different and unknown lighting conditions, our method automatically determines a radiometric response function and resolves the generalized basrelief ambiguity for estimating accurate su ..."
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Cited by 33 (8 self)
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We present a selfcalibrating photometric stereo method. From a set of images taken from a fixed viewpoint under different and unknown lighting conditions, our method automatically determines a radiometric response function and resolves the generalized basrelief ambiguity for estimating accurate surface normals and albedos. We show that color and intensity profiles, which are obtained from registered pixels across images, serve as effective cues for addressing these two calibration problems. As a result, we develop a complete autocalibration method for photometric stereo. The proposed method is useful in many practical scenarios where calibrations are difficult. Experimental results validate the accuracy of the proposed method using various realworld scenes.
Characterization of Human Faces under Illumination Variations Using Rank, Integrability, and Symmetry Constraints
, 2004
"... Photometric stereo algorithms use a Lambertian reflectance model with a varying albedo field and involve the appearances of only one object. This paper extends photometric stereo algorithms to handle all the appearances of all the objects in a class, in particular the class of human faces. Simil ..."
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Cited by 32 (10 self)
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Photometric stereo algorithms use a Lambertian reflectance model with a varying albedo field and involve the appearances of only one object. This paper extends photometric stereo algorithms to handle all the appearances of all the objects in a class, in particular the class of human faces. Similarity among all facial appearances motivates a rank constraint on the albedos and surface normals in the class. This leads to a factorization of an observation matrix that consists of exemplar images of di#erent objects under di#erent illuminations, which is beyond what can be analyzed using bilinear analysis. Bilinear analysis requires exemplar images of di#erent objects under same illuminations. To fully recover the classspecific albedos and surface normals, integrability and face symmetry constraints are employed. The proposed linear algorithm takes into account the e#ects of the varying albedo field by approximating the integrability terms using only the surface normals. As an application, face recognition under illumination variation is presented.