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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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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
PCASIFT: A more distinctive representation for local image descriptors
, 2004
"... Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image deforma ..."
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Cited by 572 (6 self)
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Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image
Frames and Stable Bases for ShiftInvariant Subspaces of . . .
, 1994
"... Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is inje ..."
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Cited by 131 (30 self)
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Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 (IR d ), and for sets X of the form X = fOE(\Delta \Gamma ff) : OE 2 \Phi; ff 2 ZZ d g; with \Phi either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT and T T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators. AMS (MOS) Subject Classifications: 42C15 Key Words: Riesz bases, stable bases, shif...
Orthonormal ShiftInvariant Wavelet Packet Decomposition and Representation
 Signal Processing
, 1995
"... In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binar ..."
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Cited by 32 (8 self)
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In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a
Learning shiftinvariant sparse representation of actions
 IEEE Conference on Computer Vision and Pattern Recognition (2010) 2630
"... A central problem in the analysis of motion capture (MoCap) data is how to decompose motion sequences into primitives. Ideally, a description in terms of primitives should facilitate the recognition, synthesis, and characterization of actions. We propose an unsupervised learning algorithm for auto ..."
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Cited by 20 (4 self)
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for automatically decomposing joint movements in human motion capture (MoCap) sequences into shiftinvariant basis functions. Our formulation models the time series data of joint movements in actions as a sparse linear combination of short basis functions (snippets), which are executed (or “activated
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 557 (36 self)
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Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal
The Lumigraph
 In Proceedings of SIGGRAPH 96
, 1996
"... This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used ..."
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Cited by 1034 (43 self)
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This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used
Hierarchical Models of Object Recognition in Cortex
, 1999
"... The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore th ..."
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Cited by 817 (84 self)
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The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, little quantitative modeling has been done in the last 15 years to explore
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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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Results 11  20
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