Results 1  10
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97
Sparse subspace clustering
 In CVPR
, 2009
"... We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all oth ..."
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Cited by 176 (9 self)
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We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under mild assumptions, the SR can be obtained ’exactly ’ by using ℓ1 optimization. The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data. We apply our subspace clustering algorithm to the problem of segmenting multiple motions in video. Experiments on 167 video sequences show that our approach significantly outperforms stateoftheart methods. 1.
MultiManifold SemiSupervised Learning
"... We study semisupervised learning when the data consists of multiple intersecting manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled data in this multimanifold setting. We then propose a semisupervised learning algorithm that separates different manifolds ..."
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Cited by 115 (8 self)
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We study semisupervised learning when the data consists of multiple intersecting manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled data in this multimanifold setting. We then propose a semisupervised learning algorithm that separates different manifolds into decision sets, and performs supervised learning within each set. Our algorithm involves a novel application of Hellinger distance and sizeconstrained spectral clustering. Experiments demonstrate the benefit of our multimanifold semisupervised learning approach. 1
Robust Subspace Segmentation by LowRank Representation
"... We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlik ..."
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Cited by 107 (16 self)
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We propose lowrank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowestrank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlike the wellknown sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at finding the lowestrank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation. 1.
Robust recovery of subspace structures by lowrank representation
 IEEE Trans. Pattern Anal. Mach. Intell
, 2013
"... Abstract—In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel o ..."
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Cited by 74 (16 self)
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Abstract—In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel objective function named LowRank Representation (LRR), which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, we prove that LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for data corrupted by arbitrary sparse errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace clustering and error correction in an efficient and effective way. Index Terms—Lowrank representation, subspace clustering, segmentation, outlier detection Ç 1
A.: Image segmentation by probabilistic bottomup aggregation and cue integration
, 2007
"... We present a parameter free approach that utilizes multiple cues for image segmentation. Beginning with an image, we execute a sequence of bottomup aggregation steps in which pixels are gradually merged to produce larger and larger regions. In each step we consider pairs of adjacent regions and pro ..."
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Cited by 66 (1 self)
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We present a parameter free approach that utilizes multiple cues for image segmentation. Beginning with an image, we execute a sequence of bottomup aggregation steps in which pixels are gradually merged to produce larger and larger regions. In each step we consider pairs of adjacent regions and provide a probability measure to assess whether or not they should be included in the same segment. Our probabilistic formulation takes into account intensity and texture distributions in a local area around each region. It further incorporates priors based on the geometry of the regions. Finally, posteriors based on intensity and texture cues are combined using a mixture of experts formulation. This probabilistic approach is integrated into a graph coarsening scheme providing a complete hierarchical segmentation of the image. The algorithm complexity is linear in the number of the image pixels and it requires almost no usertuned parameters. We test our method on a variety of gray scale images and compare our results to several existing segmentation algorithms. 1.
Unsupervised Segmentation of Natural Images via Lossy Data Compression
, 2007
"... In this paper, we cast naturalimage segmentation as a problem of clustering texture features as multivariate mixed data. We model the distribution of the texture features using a mixture of Gaussian distributions. Unlike most existing clustering methods, we allow the mixture components to be degene ..."
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Cited by 54 (3 self)
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In this paper, we cast naturalimage segmentation as a problem of clustering texture features as multivariate mixed data. We model the distribution of the texture features using a mixture of Gaussian distributions. Unlike most existing clustering methods, we allow the mixture components to be degenerate or nearlydegenerate. We contend that this assumption is particularly important for midlevel image segmentation, where degeneracy is typically introduced by using a common feature representation for different textures in an image. We show that such a mixture distribution can be effectively segmented by a simple agglomerative clustering algorithm derived from a lossy data compression approach. Using either 2D texture filter banks or simple fixedsize windows to obtain texture features, the algorithm effectively segments an image by minimizing the overall coding length of the feature vectors. We conduct comprehensive experiments to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for image segmentation. The algorithm compares favorably against other wellknown imagesegmentation methods on the Berkeley image database.
On the Role of Sparse and Redundant Representations in Image Processing
 PROCEEDINGS OF THE IEEE – SPECIAL ISSUE ON APPLICATIONS OF SPARSE REPRESENTATION AND COMPRESSIVE SENSING
, 2009
"... Much of the progress made in image processing in the past decades can be attributed to better modeling of image content, and a wise deployment of these models in relevant applications. This path of models spans from the simple ℓ2norm smoothness, through robust, thus edge preserving, measures of smo ..."
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Cited by 51 (1 self)
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Much of the progress made in image processing in the past decades can be attributed to better modeling of image content, and a wise deployment of these models in relevant applications. This path of models spans from the simple ℓ2norm smoothness, through robust, thus edge preserving, measures of smoothness (e.g. total variation), and till the very recent models that employ sparse and redundant representations. In this paper, we review the role of this recent model in image processing, its rationale, and models related to it. As it turns out, the field of image processing is one of the main beneficiaries from the recent progress made in the theory and practice of sparse and redundant representations. We discuss ways to employ these tools for various image processing tasks, and present several applications in which stateoftheart results are obtained.
Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories
 In IEEE Conference on Computer Vision and Pattern Recognition
, 2008
"... We examine the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this motion segmentation problem can be cast as the problem of segmenting samples drawn from a union of linear subspaces. Due to limitations of the ..."
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Cited by 47 (5 self)
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We examine the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this motion segmentation problem can be cast as the problem of segmenting samples drawn from a union of linear subspaces. Due to limitations of the tracker, occlusions and the presence of nonrigid objects in the scene, the obtained motion trajectories may contain grossly mistracked features, missing entries, or not correspond to any valid motion model. In this paper, we develop a robust subspace separation scheme that can deal with all of these practical issues in a unified framework. Our methods draw strong connections between lossy compression, rank minimization, and sparse representation. We test our methods extensively and compare their performance to several extant methods with experiments on the Hopkins 155 database. Our results are on par with stateoftheart results, and in many cases exceed them. All MATLAB code and segmentation results are publicly available for peer evaluation at
A geometric analysis of subspace clustering with outliers
 ANNALS OF STATISTICS
, 2012
"... This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information a ..."
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Cited by 41 (3 self)
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This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [11], which significantly broadens the range of problems where it is provably effective. For instance, we show that SSC can recover multiple subspaces, each of dimension comparable to the ambient dimension. We also prove that SSC can correctly cluster data points even when the subspaces of interest intersect. Further, we develop an extension of SSC that succeeds when the data set is corrupted with possibly overwhelmingly many outliers. Underlying our analysis are clear geometric insights, which may bear on other sparse recovery problems. A numerical study complements our theoretical analysis and demonstrates the effectiveness of these methods.