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342
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 815 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed
Local polynomial regression on unknown manifolds. Tech. rep.,Department of Statistics
 In Advances in Neural InformationProcessing Systems (NIPS
, 2006
"... Abstract: We reveal the phenomenon that “naive ” multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression functions belonging to a Sobolev space when the predic ..."
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Cited by 31 (4 self)
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the predictor variables live on or close to a lower dimensional manifold. 1.
A Blind Source Separation Technique Using Second Order Statistics
, 1997
"... Separation of sources consists in recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: the linear mixture should be `blindly' processed. This typically occurs in narrowband array pro ..."
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Cited by 336 (9 self)
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processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on stationary secondorder statistics
Manifold denoising
 Advances in Neural Information Processing Systems (NIPS) 19
, 2006
"... We consider the problem of denoising a noisily sampled submanifold M in R d, where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graphbased diffusion process of the point sample. We analyze this diffusion process us ..."
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Cited by 37 (1 self)
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We consider the problem of denoising a noisily sampled submanifold M in R d, where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graphbased diffusion process of the point sample. We analyze this diffusion process
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
 IEEE TRANS. ON SIGNAL PROCESSING
, 2004
"... In the manifold learning problem, one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper, we consider the closely related problem of estimating the manifold ..."
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Cited by 99 (5 self)
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the manifold’s intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sample points as realizations of an unknown multivariate density supported on an unknown smooth manifold. We introduce a novel geometric approach based on entropic graph methods. Although the theory
The Nielsen realization problem
 Bull. Amer. Math. Soc
, 1980
"... If M is a closed, oriented 2manifold of genus g> 2, then it admits many hyperbolic metrics (metrics of constant curvature 1). In special cases such a metric possesses a nontrivial group of symmetries, of isometries to itself. The group of isometries of a closed hyperbolic manifold is always fin ..."
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Cited by 169 (0 self)
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If M is a closed, oriented 2manifold of genus g> 2, then it admits many hyperbolic metrics (metrics of constant curvature 1). In special cases such a metric possesses a nontrivial group of symmetries, of isometries to itself. The group of isometries of a closed hyperbolic manifold is always
A general framework for motion segmentation: Independent, articulated, rigid, nonrigid, degenerate and nondegenerate
 In ECCV
, 2006
"... Abstract. We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constra ..."
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Cited by 139 (0 self)
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estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown beforehand, and segment the trajectories accordingly. It first transforms and normalizes the trajectories; secondly, for each trajectory it estimates a local linear manifold through local
Observer design for systems with unknown inputs
 INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
, 2005
"... Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along ..."
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Cited by 16 (0 self)
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Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along
Motion Estimation on the Essential Manifold
 In &quot;Computer Vision ECCV 94, Lecture Notes in Computer Sciences
, 1994
"... . We introduce a novel perspective for viewing the "egomotion reconstruction" problem as the estimation of the state of a dynamical system having an implicit measurement constraint and unknown inputs. Such a system happens to be "linear", but it is defined on a space (the " ..."
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Cited by 20 (9 self)
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. We introduce a novel perspective for viewing the "egomotion reconstruction" problem as the estimation of the state of a dynamical system having an implicit measurement constraint and unknown inputs. Such a system happens to be "linear", but it is defined on a space (the "
Manifold Learning and Applications in Recognition
 in Intelligent Multimedia Processing with Soft Computing
, 2004
"... this paper, recognition can be achieved by comparing the probability metric between each unknown sample and corresponding autoassociative sample with di#erent NAMs. Without loss of generality, the probability metric (in this paper, we use Gaussian function) between each sample x # and autoassociat ..."
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Cited by 10 (0 self)
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this paper, recognition can be achieved by comparing the probability metric between each unknown sample and corresponding autoassociative sample with di#erent NAMs. Without loss of generality, the probability metric (in this paper, we use Gaussian function) between each sample x # and auto
Results 1  10
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342