Results 1  10
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133
A geometrical framework for low level vision
 IEEE Trans. on Image Processing
, 1998
"... Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, an ..."
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Cited by 176 (35 self)
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Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, and 2D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scalespace. I.
2000, ‘Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
 ACM Symposium on Computational Geometry
"... For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described. 1. ..."
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Cited by 59 (2 self)
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For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described. 1.
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
 Acta Appl. Math
"... Abstract. We give simple formulas for the canonical metric, gradient, Lie ..."
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Cited by 49 (11 self)
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Abstract. We give simple formulas for the canonical metric, gradient, Lie
The Lipschitz continuity of the distance function to the cut locus
 Trans. Amer. Math. Soc
"... Abstract. Let N be a closed submanifold of a complete smooth Riemannian manifold M and Uν the total space of the unit normal bundle of N. Foreach v ∈ Uν,letρ(v) denote the distance from N to the cut point of N on the geodesic γv with the velocity vector ˙γv(0) = v. The continuity of the function ρ ..."
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Cited by 24 (2 self)
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Abstract. Let N be a closed submanifold of a complete smooth Riemannian manifold M and Uν the total space of the unit normal bundle of N. Foreach v ∈ Uν,letρ(v) denote the distance from N to the cut point of N on the geodesic γv with the velocity vector ˙γv(0) = v. The continuity of the function ρ on Uν is well known. In this paper we prove that ρ is locally Lipschitz on which ρ is bounded; in particular, if M and N are compact, then ρ is globally Lipschitz on Uν. Therefore, the canonical interior metric δ may be introduced on each connected component of the cut locus of N, and this metric space becomes a locally compact and complete length space. Let N be an immersed submanifold of a complete C ∞ Riemannian manifold M and π: Uν → N the unit normal bundle of N. For each positive integer k and vector v ∈ Uν, letanumberλk(v) denote the parameter value of γv, whereγv denotes the geodesic for which the velocity vector is v at t =0, such that γv(λk(v)) is the kth focal point (conjugate point for the case in which N is a point) of N along γv, counted with focal (or conjugate) multiplicities. A unit speed geodesic segment
On Random Walks on Wreath Products
 Ann. Probab
, 2001
"... Wreath products are a type of semidirect products. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to th ..."
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Cited by 23 (1 self)
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Wreath products are a type of semidirect products. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to the starting point of certain walks on wreath products is closely related to some functionals of the local times of a walk taking place on a simpler factor group.
Weighted norm inequalities, offdiagonal estimates and elliptic operators, Part II: Offdiagonal estimates on spaces of homogeneous type
, 2005
"... Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincar ..."
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Cited by 23 (6 self)
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Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities. 1. Introduction and
Isoperimetric and universal inequalities for eigenvalues, in Spectral Theory and Geometry
 London Mathematical Society Lecture Note Series
, 1999
"... PaynePólyaWeinberger conjecture, Sperner’s inequality, biharmonic operator, biLaplacian, clamped plate problem, Rayleigh’s conjecture, buckling problem, the PólyaSzegő conjecture, universal inequalities for eigenvalues, HileProtter inequality, H. C. Yang’s inequality. Short title: Isoperimetric ..."
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Cited by 20 (4 self)
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PaynePólyaWeinberger conjecture, Sperner’s inequality, biharmonic operator, biLaplacian, clamped plate problem, Rayleigh’s conjecture, buckling problem, the PólyaSzegő conjecture, universal inequalities for eigenvalues, HileProtter inequality, H. C. Yang’s inequality. Short title: Isoperimetric and Universal Inequalities This paper reviews many of the known inequalities for the eigenvalues of the Laplacian and biLaplacian on bounded domains in Euclidean space. In particular, we focus on isoperimetric inequalities for the low eigenvalues of the Dirichlet and Neumann Laplacians and of the vibrating clamped plate problem (i.e., the biharmonic operator with “Dirichlet ” boundary conditions). We also discuss the known universal inequalities for the eigenvalues of the Dirichlet Laplacian and the vibrating clamped plate and buckling problems and go on to
Várilly, “Dixmier traces on noncompact isospectral deformations
 J. Funct. Anal
"... We extend the isospectral deformations of Connes, Landi and DuboisViolette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R l. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of fu ..."
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Cited by 18 (8 self)
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We extend the isospectral deformations of Connes, Landi and DuboisViolette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R l. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of R l, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.