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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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. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
A Survey of Computer VisionBased Human Motion Capture
 Computer Vision and Image Understanding
, 2001
"... A comprehensive survey of computer visionbased human motion capture literature from the past two decades is presented. The focus is on a general overview based on a taxonomy of system functionalities, broken down into four processes: initialization, tracking, pose estimation, and recognition. Each ..."
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Cited by 508 (14 self)
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A comprehensive survey of computer visionbased human motion capture literature from the past two decades is presented. The focus is on a general overview based on a taxonomy of system functionalities, broken down into four processes: initialization, tracking, pose estimation, and recognition. Each process is discussed and divided into subprocesses and/or categories of methods to provide a reference to describe and compare the more than 130 publications covered by the survey. References are included throughout the paper to exemplify important issues and their relations to the various methods. A number of general assumptions used in this research field are identified and the character of these assumptions indicates that the research field is still in an early stage of development. To evaluate the state of the art, the major application areas are identified and performances are analyzed in light of the methods
Perturbative gauge theory as a string theory in twistor space
 Commun. Math. Phys
"... Perturbative scattering amplitudes in YangMills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed ..."
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Cited by 388 (0 self)
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Perturbative scattering amplitudes in YangMills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of N = 4 super YangMills theory and the Dinstanton expansion of a certain string theory, namely the topological B model whose target space is the CalabiYau supermanifold CP 34. December
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