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Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
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The Gradient Flow of �
, 2006
"... M Rm2 We study the gradient flow of the Riemannian functional F(g):= M Rm2. This flow corresponds to a fourthorder degenerate parabolic equation for a Riemannian metric. We prove that, as with the Ricci flow, the degeneracies may be accounted for entirely by diffeomorphism flow, and hence we sh ..."
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Cited by 11 (5 self)
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M Rm2 We study the gradient flow of the Riemannian functional F(g):= M Rm2. This flow corresponds to a fourthorder degenerate parabolic equation for a Riemannian metric. We prove that, as with the Ricci flow, the degeneracies may be accounted for entirely by diffeomorphism flow, and hence we
Gradient flows and geometric active contour models
 in Proc. of the 5th International Conference on Computer Vision
, 1995
"... In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature of interes ..."
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Cited by 239 (19 self)
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In this paper, we analyze the geometric active contour models discussed in [6, 181 from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel snake paradigm in which the feature
Snakes, Shapes, and Gradient Vector Flow
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new extern ..."
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Cited by 757 (16 self)
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external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a graylevel or binary edge map derived from the image. It differs fundamentally from traditional snake external forces
Affine Invariant Gradient Flows
"... Introduction A number of problems in image processing and computer vision are approached via energy minimization techniques. The minimizer can be obtained for example via gradient descent flows, which are flows minimizing this energy as fast as possible according to certain metric. In a number of c ..."
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Cited by 1 (0 self)
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Introduction A number of problems in image processing and computer vision are approached via energy minimization techniques. The minimizer can be obtained for example via gradient descent flows, which are flows minimizing this energy as fast as possible according to certain metric. In a number
THE GRADIENT FLOW MOTION OF BOUNDARY VORTICES
, 2005
"... Abstract. We consider the gradient flow of an energy functional describing boundary vortices in thin magnetic films. We obtain motion laws for the singularities in all time scalings by using the method of Γconvergence of gradient flows. Contents ..."
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Cited by 2 (1 self)
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Abstract. We consider the gradient flow of an energy functional describing boundary vortices in thin magnetic films. We obtain motion laws for the singularities in all time scalings by using the method of Γconvergence of gradient flows. Contents
Gradient flows in asymmetric metric spaces
 In preparation
"... This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is e ..."
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Cited by 5 (4 self)
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This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows
The gradient flow in a twisted box
"... We study the perturbative behavior of the gradient flow in a twisted box. We apply this information to define a running coupling using the energy density of the flow field. We study the stepscaling function and the size of cutoff effects in SU(2) pure gauge theory. We conclude that the twisted gra ..."
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Cited by 4 (0 self)
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We study the perturbative behavior of the gradient flow in a twisted box. We apply this information to define a running coupling using the energy density of the flow field. We study the stepscaling function and the size of cutoff effects in SU(2) pure gauge theory. We conclude that the twisted
Renormalizability of the gradient flow in the 2D
, 2014
"... It is known that the gauge field and its composite operators evolved by the Yang–Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) nonlinear sigma model possesses a similar property ..."
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It is known that the gauge field and its composite operators evolved by the Yang–Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) nonlinear sigma model possesses a similar
A Variational Principle For Gradient Flows
, 2004
"... We verify  after appropriate modifications  an old conjecture of BrezisEkeland ([3], [4]) concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of gradient flows for convex energy functionals. Our approach is based on a concept of "selfd ..."
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Cited by 34 (25 self)
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We verify  after appropriate modifications  an old conjecture of BrezisEkeland ([3], [4]) concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of gradient flows for convex energy functionals. Our approach is based on a concept of "
Results 1  10
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