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Journal ArticleDOI

Robust Face Recognition via Sparse Representation

TL;DR: This work considers the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise, and proposes a general classification algorithm for (image-based) object recognition based on a sparse representation computed by C1-minimization.
Abstract: We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

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Citations
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Journal ArticleDOI
TL;DR: It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, it is proved that under certain conditions LRR can exactly recover the row space of the original data.
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 Low-Rank 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.

3,085 citations


Cites background from "Robust Face Recognition via Sparse ..."

  • ...near) subspaces are possibly the most common choice, mainly because they are easy to compute and often effective in real applications. Several types of visual data, such as motion [1], [2], [3], face [4] and texture [5], have been known to be well characterized by subspaces. Moreover, by applying the concept of reproducing kernel Hilbert space [6], one can easily extend the linear models to handle no...

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  • ...) data into clusters with each cluster corresponding to a subspace. Subspace segmentation is an important data clustering problem and arises in numerous research areas, including computer vision [3], [4], [10], [11], image processing [5], [12], [13], machine learning [14], [15] and system identification [16]. When the data is clean, i.e., the samples are strictly drawn from the subspaces, several exis...

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Journal ArticleDOI
TL;DR: This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Abstract: Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

2,784 citations


Cites methods from "Robust Face Recognition via Sparse ..."

  • ...ly few incoherent random measurements [12, 8, 9, 7, 2, 43]. The sparse solution ˘ to Eq. 1 may also be used for sparse classification schemes, such as the sparse representation for classification (SRC) [44]. Importantly, the compressive sensing and sparse representation architectures are convex and scale well to large problems, as opposed to brute-force combinatorial alternatives. 3 3 Sparse identificati...

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Journal ArticleDOI
TL;DR: In this article, a sparse subspace clustering algorithm is proposed to cluster high-dimensional data points that lie in a union of low-dimensional subspaces, where a sparse representation corresponds to selecting a few points from the same subspace.
Abstract: Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.

2,298 citations

Proceedings ArticleDOI
06 Nov 2011
TL;DR: This paper indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification, and proposes a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS).
Abstract: As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l 1 -norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.

2,001 citations


Cites background from "Robust Face Recognition via Sparse ..."

  • ...In [8], Wright et al. reported a very interesting work by using sparse representation for robust face recognition (FR)....

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Journal ArticleDOI
29 Apr 2010
TL;DR: This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.
Abstract: Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-the-art results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.

1,871 citations


Cites methods from "Robust Face Recognition via Sparse ..."

  • ...The answer has been largely positive: in the past few years, variations and extensions of `1 minimization have been applied to many vision tasks, including ∗John Wright and Yi Ma are with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign....

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References
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Journal ArticleDOI
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

40,785 citations


Additional excerpts

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Book
Vladimir Vapnik1
01 Jan 1995
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

40,147 citations


"Robust Face Recognition via Sparse ..." refers background in this paper

  • ...What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed....

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Book
01 Mar 2004
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

33,341 citations

Journal ArticleDOI
TL;DR: A near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals, and that is easy to implement using a neural network architecture.
Abstract: We have developed a near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals. The computational approach taken in this system is motivated by both physiology and information theory, as well as by the practical requirements of near-real-time performance and accuracy. Our approach treats the face recognition problem as an intrinsically two-dimensional (2-D) recognition problem rather than requiring recovery of three-dimensional geometry, taking advantage of the fact that faces are normally upright and thus may be described by a small set of 2-D characteristic views. The system functions by projecting face images onto a feature space that spans the significant variations among known face images. The significant features are known as "eigenfaces," because they are the eigenvectors (principal components) of the set of faces; they do not necessarily correspond to features such as eyes, ears, and noses. The projection operation characterizes an individual face by a weighted sum of the eigenface features, and so to recognize a particular face it is necessary only to compare these weights to those of known individuals. Some particular advantages of our approach are that it provides for the ability to learn and later recognize new faces in an unsupervised manner, and that it is easy to implement using a neural network architecture.

14,562 citations


"Robust Face Recognition via Sparse ..." refers background in this paper

  • ...…dictionary of base elements or signal atoms has seen a recent surge of interest [9], [10], [11], [12].1 Much of this excitement centers around the discovery that whenever the optimal representation is sufficiently sparse, it can be efficiently computed by convex optimization [9], even though…...

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Journal ArticleDOI
TL;DR: A face recognition algorithm which is insensitive to large variation in lighting direction and facial expression is developed, based on Fisher's linear discriminant and produces well separated classes in a low-dimensional subspace, even under severe variations in lighting and facial expressions.
Abstract: We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a high-dimensional 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 self-shadowing, 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 low-dimensional subspace, even under severe variation in lighting and facial expressions. The eigenface technique, another method based on linearly projecting the image space to a low dimensional subspace, has similar computational requirements. Yet, extensive experimental results demonstrate that the proposed "Fisherface" method has error rates that are lower than those of the eigenface technique for tests on the Harvard and Yale face databases.

11,674 citations


"Robust Face Recognition via Sparse ..." refers background or methods in this paper

  • ...One class of methods extracts holistic face features such as Eigenfaces[23], Fisherfaces [ 24 ], and Laplacianfaces [25]....

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  • ...high-dimensional test image into lower dimensional feature spaces: examples include Eigenfaces [23], Fisherfaces [ 24 ], Laplacianfaces [25], and a host of variants [26], [27]....

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  • ...the other features because the maximal number of valid Fisherfaces is one less than the number of classes k [ 24 ], 38 in this case....

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  • ...Subspace models are flexible enough to capture much of the variation in real data sets and are especially well motivated in the context of face recognition, where it has been observed that the images of faces under varying lighting and expression lie on a special low-dimensional subspace [ 24 ], [30], often called a face subspace....

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Trending Questions (1)
What is the minimum number of images required for a facial recognition model to sufficiently learn features?

The paper does not provide a specific minimum number of images required for a facial recognition model to sufficiently learn features.