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A SubdivisionBased Algorithm for the Sparse Resultant
 J. ACM
, 1999
"... Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all common roots to a problem in linear algebra. ..."
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Cited by 42 (8 self)
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Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all common roots to a problem in linear algebra.
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (8 self)
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This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal
Dynamic Subdivisionbased Solid Modeling
, 2000
"... This survey paper discusses the stateoftheart in solid modeling, subdivision modeling, and physicsbased modeling. Although related to each other, these research areas have yet to be integrated into a single framework. We present a historical review of each area separately, discuss research that ..."
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Cited by 4 (0 self)
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and shortcomings. Subdivision modeling uses procedural algorithms to recursively define smooth curves, surfaces, and solids. We show the connections between subdivision modeling and splinebased modeling and demonstrate that the former is actually a generalization of the latter. Physicsbased modeling augments
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Efficient sparse coding algorithms
 In NIPS
, 2007
"... Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we ..."
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Cited by 440 (14 self)
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present efficient sparse coding algorithms that are based on iteratively solving two convex optimization problems: an L1regularized least squares problem and an L2constrained least squares problem. We propose novel algorithms to solve both of these optimization problems. Our algorithms result in a
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The KSVD algorithm
SubdivisionBased Surface Representations
"... Subdivision can be thought of as a natural extension of existing patchbased surface representations. In this view, subdivision algorithms effectively bridge the gap between patchbased and polygonal mesh representations. Using subdivision also naturally leads to useful multiresolution representation ..."
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. In our ongoing work we are addressing a few important research problems that have to be solved to make such applications practical. Currently our research is focused on two major issues: the design of efficient algorithms for manipulation of subdivisionbased multiresolution surfaces and development
Behavior recognition via sparse spatiotemporal features
 In VSPETS
, 2005
"... A common trend in object recognition is to detect and leverage the use of sparse, informative feature points. The use of such features makes the problem more manageable while providing increased robustness to noise and pose variation. In this work we develop an extension of these ideas to the spatio ..."
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Cited by 705 (4 self)
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to the spatiotemporal case. For this purpose, we show that the direct 3D counterparts to commonly used 2D interest point detectors are inadequate, and we propose an alternative. Anchoring off of these interest points, we devise a recognition algorithm based on spatiotemporally windowed data. We present
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Results 1  10
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