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111
From Few to many: Illumination cone models for face recognition under variable lighting and pose
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a generative appearancebased method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a smal ..."
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Cited by 754 (12 self)
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We present a generative appearancebased method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render—or synthesize—images of the face under novel poses and illumination conditions. The pose space is then sampled, and for each pose the corresponding illumination cone is approximated by a lowdimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone (based on Euclidean distance within the image space). We test our face recognition method on 4050 images from the Yale Face Database B; these images contain 405 viewing conditions (9 poses ¢ 45 illumination conditions) for 10 individuals. The method performs almost without error, except on the most extreme lighting directions, and significantly outperforms popular recognition methods that do not use a generative model.
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...
The CMU Pose, Illumination, and Expression Database
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... In the Fall of 2000 we collected a database of over 40,000 facial images of 68 people. Using the CMU 3D Room we imaged each person across 13 different poses, under 43 different illumination conditions, and with 4 different expressions. We call this the CMU Pose, Illumination, and Expression (PIE) da ..."
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Cited by 367 (7 self)
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In the Fall of 2000 we collected a database of over 40,000 facial images of 68 people. Using the CMU 3D Room we imaged each person across 13 different poses, under 43 different illumination conditions, and with 4 different expressions. We call this the CMU Pose, Illumination, and Expression (PIE) database. We describe the imaging hardware, the collection procedure, the organization of the images, several possible uses, and how to obtain the database.
Acquiring linear subspaces for face recognition under variable lighting
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in ..."
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Cited by 317 (2 self)
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Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in one of three ways: A large set of images of the object under different lighting conditions is acquired, and principal component analysis (PCA) is used to estimate a subspace. Alternatively, synthetic images are rendered from a 3D model (perhaps reconstructed from images) under point sources, and again PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a lowdimensional linear space, and that this subspace is close to those acquired by the other methods. More specifically, there exist configurations of k point light source directions, with k typically ranging from 5 to 9, such that by taking k images of an object under these single sources, the resulting subspace is an effective representation for recognition under a wide range of lighting conditions. Since the subspace is generated directly from real images, potentially complex and/or brittle intermediate steps such as 3D reconstruction can be completely avoided; nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse (harmonic) light fields. We validate the use of subspaces constructed in this fashion within the context of face recognition.
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.
The CMU Pose, Illumination, and Expression (PIE) Database
, 2002
"... Between October 2000 and December 2000 we collected a database of over 40,000 facial images of 68 people. Using the CMU 3D Room we imaged each person across 13 different poses, under 43 different illumination conditions, and with 4 different expressions. We call this database the CMU Pose, Illuminat ..."
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Cited by 235 (6 self)
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Between October 2000 and December 2000 we collected a database of over 40,000 facial images of 68 people. Using the CMU 3D Room we imaged each person across 13 different poses, under 43 different illumination conditions, and with 4 different expressions. We call this database the CMU Pose, Illumination, and Expression (PIE) database. In this paper we describe the imaging hardware, the collection procedure, the organization of the database, several potential uses of the database, and how to obtain the database.
Clustering appearances of objects under varying illumination conditions
 In CVPR
, 2003
"... We introduce two appearancebased methods for clustering a set of images of 3D objects, acquired under varying illumination conditions, into disjoint subsets corresponding to individual objects. The first algorithm is based on the concept of illumination cones. According to the theory, the clusteri ..."
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Cited by 117 (3 self)
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We introduce two appearancebased methods for clustering a set of images of 3D objects, acquired under varying illumination conditions, into disjoint subsets corresponding to individual objects. The first algorithm is based on the concept of illumination cones. According to the theory, the clustering problem is equivalent to finding convex polyhedral cones in the highdimensional image space. To efficiently determine the conic structures hidden in the image data, we introduce the concept of conic affinity which measures the likelihood of a pair of images belonging to the same underlying polyhedral cone. For the second method, we introduce another affinity measure based on image gradient comparisons. The algorithm operates directly on the image gradients by comparing the magnitudes and orientations of the image gradient at each pixel. Both methods have clear geometric motivations, and they operate directly on the images without the need for feature extraction or computation of pixel statistics. We demonstrate experimentally that both algorithms are surprisingly effective in clustering images acquired under varying illumination conditions with two large, wellknown image data sets. 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 ..."
Computing gaussian mixture models with EM using equivalence constraints
 In Advances in Neural Information Processing Systems 16
, 2003
"... Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, ..."
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Cited by 103 (12 self)
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Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information. 1
AppearanceBased Face Recognition and LightFields
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... Arguably the most important decision to be made when developing an object recognition algorithm is selecting the scene measurements or features on which to base the algorithm. In appearancebased object recognition the features are chosen to be the pixel intensity values in an image of the object. T ..."
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Cited by 93 (4 self)
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Arguably the most important decision to be made when developing an object recognition algorithm is selecting the scene measurements or features on which to base the algorithm. In appearancebased object recognition the features are chosen to be the pixel intensity values in an image of the object. These pixel intensities correspond directly to the radiance of light emitted from the object along certain rays in space. The set of all such radiance values over all possible rays is known as the plenoptic function or lightfield. In this paper we develop the theory of appearancebased object recognition from lightfields. This theory leads directly to a poseinvariant face recognition algorithm that uses as many images of the face as are available, from one upwards. All of the pixels, whichever image they come from, are treated equally and used to estimate the (eigen) lightfield of the object. The eigen lightfield is then used as the set of features on which to base recognition, analogously to how the pixel intensities are used in appearancebased object recognition. We also show how our algorithm can be extended to recognize faces across pose and illumination by using Fisher lightfields.