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WHICH MEASURES ARE PROJECTIONS OF PURELY UNRECTIFIABLE ONEDIMENSIONAL HAUSDORFF MEASURES
"... Abstract. We give a necessary and sufficient condition for a measure µ on the real line to be an orthogonal projection of H1 A for some purely 1unrectifiable planar set A. 1. ..."
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Abstract. We give a necessary and sufficient condition for a measure µ on the real line to be an orthogonal projection of H1 A for some purely 1unrectifiable planar set A. 1.
For a set K we denote by H 1 (K) the one dimensional Hausdorff measure, which we call Hausdorff
, 2006
"... We discuss 1Ahlforsregular connected sets in a metric space. We prove that such a set is ‘flat ’ on most scales and locations. We give a quantitative version of this. This, together with work of I. Hahlomaa, gives a characterization of 1Ahlfors regular subsets of 1Ahlforsregular curves in a met ..."
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We discuss 1Ahlforsregular connected sets in a metric space. We prove that such a set is ‘flat ’ on most scales and locations. We give a quantitative version of this. This, together with work of I. Hahlomaa, gives a characterization of 1Ahlfors regular subsets of 1Ahlforsregular curves in a metric space, generalizing in a way the Analyst’s (Geometric) Traveling Salesman theorems by P. Jones, K. Okikiolu, and G. DavidS. Semmes for sets in R d. Our results may be stated in terms of average Menger Curvature. 1
Steiner’s invariant and minimal connections
 Portugal. Math. (N.S
"... Abstract. The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the onedimensional Hausdorff measure. 1. ..."
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Cited by 1 (0 self)
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Abstract. The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the onedimensional Hausdorff measure. 1.
Comparing Images Using the Hausdorff Distance
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide ef ..."
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Cited by 658 (10 self)
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The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide
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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in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a onedimensional tran...
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 590 (13 self)
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study separately. We show that the size of the oscillations can be measured from the wavelet transform local maxima. It has been shown that one and twodimensional signals can be reconstructed from the local maxima of their wavelet transform [14]. As an application, we develop an algorithm that removes
Shape Matching and Object Recognition Using Shape Contexts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform ..."
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Cited by 1787 (21 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 566 (11 self)
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We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 537 (6 self)
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Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a
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