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42
M.: Weighted minimal hypersurface reconstruction
 IEEE TPAMI 29(7) (Jul
"... Abstract—Many problems in computer vision can be formulated as a minimization problem for an energy functional. If this functional is given as an integral of a scalarvalued weight function over an unknown hypersurface, then the soughtafter minimal surface can be determined as a solution of the fun ..."
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Cited by 19 (2 self)
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existing proofs. Our work opens up the possibility of solving problems involving minimal hypersurfaces in a dimension higher than three, which were previously impossible to solve in practice. We also introduce two applications of our new framework: We show how to reconstruct temporally coherent geometry
IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1 Weighted Minimal Hypersurface Reconstruction
, 2006
"... Many problems in computer vision can be formulated as a minimization problem for an energy functional. If this functional is given as an integral of a scalarvalued weight function over an unknown hypersurface, then the soughtafter minimal surface can be determined as a solution of the functional’s ..."
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existing proofs. Our work opens up the possibility to solve problems involving minimal hypersurfaces in dimension higher than three, which were previously impossible to solve in practice. We also introduce two applications of our new framework: we show how to reconstruct temporally coherent geometry from
A Theory of Networks for Approximation and Learning
 Laboratory, Massachusetts Institute of Technology
, 1989
"... Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, t ..."
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Cited by 235 (24 self)
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Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view
Associated forms and hypersurface singularities: the binary case, preprint
"... Abstract. In the recent articles [EI] and [AI], it was conjectured that all rational GLninvariant functions of forms of degree d ≥ 3 on Cn can be extracted, in a canonical way, from those of forms of degree n(d−2) by means of assigning every form with nonvanishing discriminant the socalled associa ..."
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Cited by 3 (1 self)
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called associated form. While this surprising statement is interesting from the point of view of classical invariant theory, its original motivation was the reconstruction problem for isolated hypersurface singularities, which is the problem of finding a constructive proof of the wellknown MatherYau theorem
The Calderón problem for conormal potentials, I: Global uniqueness and reconstruction
 Comm. Pure Appl. Math
"... The goal of this paper is to establish global uniqueness and obtain reconstruction, in dimensions n ≥ 3, for the Calderón problem in the class of potentials conormal to a smooth submanifold H in R n. In the case of hypersurfaces, the potentials considered here may have any singularity weaker than th ..."
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Cited by 31 (21 self)
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The goal of this paper is to establish global uniqueness and obtain reconstruction, in dimensions n ≥ 3, for the Calderón problem in the class of potentials conormal to a smooth submanifold H in R n. In the case of hypersurfaces, the potentials considered here may have any singularity weaker than
Regularization networks: fast weight calculation via Kalman filtering
"... Regularization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. Their main drawback is that the computation of the weights scales as O(n3) where n is the number of data. In this paper we s ..."
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Regularization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. Their main drawback is that the computation of the weights scales as O(n3) where n is the number of data. In this paper we
Spacetime Isosurface Evolution for Temporally Coherent 3D Reconstruction
 In International Conference on Computer Vision and Pattern Recognition
, 2004
"... We model the dynamic geometry of a timevarying scene as a 3D isosurface in spacetime. The intersection of the isosurface with planes of constant time yields the geometry at a single time instant. An optimal fit of our model to multiple video sequences is defined as the minimum of an energy functio ..."
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Cited by 40 (5 self)
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functional. This functional is given by an integral over the entire hypersurface, which is designed to optimize photoconsistency. A PDEbased evolution derived from the EulerLagrange equation maximizes consistency with all of the given video data simultaneously. The result is a 3D model of the scene which
Spacetimecoherent Geometry Reconstruction from Multiple Video Streams
"... By reconstructing timevarying geometry one frame at a time, one ignores the continuity of natural motion, wasting useful information about the underlying videoimage formation process and taking into account temporally discontinuous reconstruction results. In 4D spacetime, the surface of a dynamic ..."
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Cited by 10 (0 self)
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By reconstructing timevarying geometry one frame at a time, one ignores the continuity of natural motion, wasting useful information about the underlying videoimage formation process and taking into account temporally discontinuous reconstruction results. In 4D spacetime, the surface of a dynamic
A Kalman filtering algorithm for regularization networks
 In Proc. American Control Conference
, 2000
"... obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. With the usual algorithm, the computation of the weights scales as O(n 3) where n is the number of data. In this paper we show that for a class of monodimensional problems, the ..."
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Cited by 2 (0 self)
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obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. With the usual algorithm, the computation of the weights scales as O(n 3) where n is the number of data. In this paper we show that for a class of monodimensional problems
Results 1  10
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