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From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Support vector machine active learning for image retrieval
, 2001
"... Relevance feedback is often a critical component when designing image databases. With these databases it is difficult to specify queries directly and explicitly. Relevance feedback interactively determinines a user’s desired output or query concept by asking the user whether certain proposed images ..."
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Cited by 448 (29 self)
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Relevance feedback is often a critical component when designing image databases. With these databases it is difficult to specify queries directly and explicitly. Relevance feedback interactively determinines a user’s desired output or query concept by asking the user whether certain proposed images
A Probabilistic Model of Information Retrieval: Development and Status
, 1998
"... The paper combines a comprehensive account of the probabilistic model of retrieval with new systematic experiments on TREC Programme material. It presents the model from its foundations through its logical development to cover more aspects of retrieval data and a wider range of system functions. Eac ..."
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Cited by 358 (25 self)
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The paper combines a comprehensive account of the probabilistic model of retrieval with new systematic experiments on TREC Programme material. It presents the model from its foundations through its logical development to cover more aspects of retrieval data and a wider range of system functions. Each step in the argument is matched by comparative retrieval tests, to provide a single coherent account of a major line of research. The experiments demonstrate, for a large test collection, that the probabilistic model is effective and robust, and that it responds appropriately, with major improvements in performance, to key features of retrieval situations.
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
, 1991
"... This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set o ..."
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Cited by 307 (2 self)
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of a complex object in 3D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. We show how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects
Boosting sparse representations for image retrieval
, 2000
"... we developed and implemented a method for creating sparse representations of real images for image retrieval. Feature selection occurs both offline by choosing highly selective features and online via “boosting”. A tree of repeated filtering with simple kernels is used to compute the initial set of ..."
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Cited by 1 (0 self)
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we developed and implemented a method for creating sparse representations of real images for image retrieval. Feature selection occurs both offline by choosing highly selective features and online via “boosting”. A tree of repeated filtering with simple kernels is used to compute the initial set
UNSUPERVISED FEATURE LEARNING VIA SPARSE HIERARCHICAL REPRESENTATIONS
"... Machine learning has proved a powerful tool for artificial intelligence and data mining problems. However, its success has usually relied on having a good feature representation of the data, and having a poor representation can severely limit the performance of learning algorithms. These feature rep ..."
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Cited by 2 (0 self)
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, such as images, audio, text, and robotic sensors. Specifically, I will first describe how efficient sparse coding algorithms — which represent each input example using a small number of basis vectors — can be used to learn good lowlevel representations from unlabeled data. I also show that this gives feature
Results 1  10
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2,121