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MOMENT MATRIX OF SELFSIMILAR MEASURES
"... Abstract. We give in this paper an expression for the moment matrix associated to a selfsimilar measure given by an Iterated Function Systems (IFS). This expression translates the selfsimilarity property of a measure to its moment matrix. This matrix relation shows that the properties of a measure ..."
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Abstract. We give in this paper an expression for the moment matrix associated to a selfsimilar measure given by an Iterated Function Systems (IFS). This expression translates the selfsimilarity property of a measure to its moment matrix. This matrix relation shows that the properties of a
MEASURES WITH ZEROS IN THE INVERSE OF THEIR MOMENT MATRIX
, 2008
"... We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure µ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that t ..."
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Cited by 4 (3 self)
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We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure µ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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matrix inequality (LMI) problems. A notion of KarushKuhnTucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided.
Noisy Word Recognition Using Denoising and Moment Matrix
"... We consider the problem of recognition of a printed word belonging to a limited dictionary. The main difficulty comes from the fact that this word can be printed using different fonts, sizes, and positions on the page. Invariant moment methods for word recognition developed by Hu [5] and Li [6] are ..."
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] are unreliable when the quality of the word image is degraded by noise. In this paper we investigate the effectivenes of simple median filter denoising for preprocessing noise degraded images prior to moment based classification using the moment matrix discriminants introduced by Hero etal [4]. 1.
Approximate moment matrix decomposition in wavelet Galerkin BEM
"... We present an improvement to the wavelet Galerkin BEM in [J. Tausch, A variable order wavelet method for the sparse representation of layer potentials in the nonstandard form. J. Numer. Math. 12(3):233{254, 2004]. In the nonstandard form representation of integral operators the number of wavelets ..."
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in every level determines the eciency of the underlying Galerkin scheme. In order to increase this number, the partial singular value decomposition (PSVD) of the moment matrix is employed. Since the resulting wavelets do not exactly satisfy the conventional vanishing moment condition, i.e., a certain
A Moment Matrix Approach to Multivariable Cubature
"... We develop an approach to multivariable cubature based on positivity, extension, and completion properties of moment matrices. We obtain a matrixbased lower bound on the size of a cubature rule of degree 2n+1; for a planar measure µ, the bound is based on estimating ρ(C): = inf{rank (T−C): T Toepl ..."
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Cited by 8 (5 self)
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We develop an approach to multivariable cubature based on positivity, extension, and completion properties of moment matrices. We obtain a matrixbased lower bound on the size of a cubature rule of degree 2n+1; for a planar measure µ, the bound is based on estimating ρ(C): = inf{rank (T
INFERENCES USING A STRUCTURED FOURTHORDER MOMENT MATRIX
"... SUMMARY. In this paper, we consider a parameterization for the fourthorder moment matrix of a random vector. This parameterization includes that of an elliptical distribution as a special case and can be used in the construction of robust tests for covariance matrices. Consistent estimates of the ..."
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SUMMARY. In this paper, we consider a parameterization for the fourthorder moment matrix of a random vector. This parameterization includes that of an elliptical distribution as a special case and can be used in the construction of robust tests for covariance matrices. Consistent estimates
An affine invariant interest point detector
 In Proceedings of the 7th European Conference on Computer Vision
, 2002
"... Abstract. This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of ..."
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Cited by 1467 (55 self)
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of the neighbourhood of an interest point. Our approach allows to solve for these problems simultaneously. It is based on three key ideas: 1) The second moment matrix computed in a point can be used to normalize a region in an affine invariant way (skew and stretch). 2) The scale of the local structure is indicated
Formal orthogonal polynomials for an arbitrary moment matrix and Lanczos type methods
, 1994
"... We give a framework for formal orthogonal polynomials with respect to an arbitrary moment matrix. When the moment matrix is Hankel, this simplies to the classical framework. The relation with Pade approximation and with Krylov subspace methods is given. 1 Formal block orthogonal polynomials We cons ..."
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Cited by 1 (1 self)
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We give a framework for formal orthogonal polynomials with respect to an arbitrary moment matrix. When the moment matrix is Hankel, this simplies to the classical framework. The relation with Pade approximation and with Krylov subspace methods is given. 1 Formal block orthogonal polynomials We
Results 1  10
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