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A Robust Subspace Approach to Layer Extraction
, 2002
"... Representing images with layers has many important applications, such as video compression, motion analysis, and 3D scene analysis. This paper presents a robust subspace approach to reliably extracting layers from images by taking advantages of the fact that homographies induced by planar patches in ..."
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Cited by 64 (6 self)
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in the scene form a low dimensional linear subspace. Such subspace provides not only a feature space where layers in the image domain are mapped onto denser and betterdefined clusters, but also a constraint for detecting outliers in the local measurements, thus making the algorithm robust to outliers
Clustering disjoint subspaces via sparse representation
 in IEEE International Conference on Acoustics, Speech, and Signal Processing
, 2010
"... Given a set of data points drawn from multiple lowdimensional linear subspaces of a highdimensional space, we consider the problem of clustering these points according to the subspaces they belong to. Our approach exploits the fact that each data point can be written as a sparse linear combination ..."
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Cited by 26 (8 self)
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Given a set of data points drawn from multiple lowdimensional linear subspaces of a highdimensional space, we consider the problem of clustering these points according to the subspaces they belong to. Our approach exploits the fact that each data point can be written as a sparse linear
SUBSPACE CLUSTERING
"... Find k lowdimensional linear subspaces to approximate a set of unlabeled data points. • kmeans objective: minC cost(C;X), where cost(C;X) = ∑ni=1 minkj=1 d2(xi,Sj)/n. DIFFERENTIAL PRIVACY Definition. A randomized algorithm A is (ε, δ)differentially private if for all X,Y satisfying d(X,Y) = 1 ..."
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Find k lowdimensional linear subspaces to approximate a set of unlabeled data points. • kmeans objective: minC cost(C;X), where cost(C;X) = ∑ni=1 minkj=1 d2(xi,Sj)/n. DIFFERENTIAL PRIVACY Definition. A randomized algorithm A is (ε, δ)differentially private if for all X,Y satisfying d(X,Y) = 1
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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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
MultiFrame Correspondence Estimation Using Subspace Constraints
, 2002
"... When a rigid scene is imaged by a moving camera, the set of all displacements of all points across multiple frames often resides in a lowdimensional linear subspace. Linear subspace constraints have been used successfully in the past for recovering 3D structure and 3D motion information from multi ..."
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Cited by 47 (8 self)
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When a rigid scene is imaged by a moving camera, the set of all displacements of all points across multiple frames often resides in a lowdimensional linear subspace. Linear subspace constraints have been used successfully in the past for recovering 3D structure and 3D motion information from
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 654 (15 self)
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, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A
Efficient PointtoSubspace Query in ℓ 1: Theory and Applications in Computer Vision ∗
"... Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of lowdimensional linear subspaces in a highdimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in ℓ ..."
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Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of lowdimensional linear subspaces in a highdimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in ℓ
Greedy subspace clustering
 In NIPS
, 2014
"... We consider the problem of subspace clustering: given points that lie on or near the union of many lowdimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric struct ..."
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Cited by 3 (0 self)
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We consider the problem of subspace clustering: given points that lie on or near the union of many lowdimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric
Visual Exploration of HighDimensional Data through Subspace Analysis and Dynamic Projections
"... We introduce a novel interactive framework for visualizing and exploring highdimensional datasets based on subspace analysis and dynamic projections. We assume the highdimensional dataset can be represented by a mixture of lowdimensional linear subspaces with mixed dimensions, and provide a metho ..."
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We introduce a novel interactive framework for visualizing and exploring highdimensional datasets based on subspace analysis and dynamic projections. We assume the highdimensional dataset can be represented by a mixture of lowdimensional linear subspaces with mixed dimensions, and provide a
Results 11  20
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