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Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
Abstract

Cited by 1505 (18 self)
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We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images of a particular face, under varying illumination but fixed pose, lie in a 3D linear subspace of the high dimensional image space  if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce selfshadowing, images will deviate from this linear subspace. Rather than explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation. Our projection method is based on Fisher's Linear Discriminant and produces well separated classes in a lowdimensional subspace even under severe variation in lighting and facial expressions. The Eigenface
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 133 (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.
Dense photometric stereo: A markov random field approach
, 2006
"... We address the problem of robust normal reconstruction by dense photometric stereo, in the presence of complex geometry, shadows, highlight, transparencies, variable attenuation in light intensities, and inaccurate estimation in light directions. The input is a dense set of noisy photometric images, ..."
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Cited by 8 (2 self)
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We address the problem of robust normal reconstruction by dense photometric stereo, in the presence of complex geometry, shadows, highlight, transparencies, variable attenuation in light intensities, and inaccurate estimation in light directions. The input is a dense set of noisy photometric images, conveniently captured by using a very simple setup consisting of a digital video camera, a reflective mirror sphere, and a handheld spotlight. We formulate the dense photometric stereo problem as a Markov network, and investigate two important inference algorithms for Markov Random Fields (MRFs) – graph cuts and belief propagation – to optimize for the most likely setting for each node in the network. In the graph cut algorithm, the MRF formulation is translated into one of energy minimization. A discontinuitypreserving metric is introduced as the compatibility function, which allows αexpansion to perform efficiently the maximum a posteriori (MAP) estimation. Using the identical dense input and the same MRF formulation, our tensor belief propagation algorithm recovers faithful normal directions, preserves underlying discontinuities, improves the normal estimation from one of discrete to continuous, and drastically reduces the storage requirement and running time. Both algorithms produce comparable and very faithful normals for complex scenes. Although the discontinuitypreserving metric in graph cuts permits efficient inference of optimal discrete labels with a theoretical