Results 231 to 240 of about 119,664 (268)

Mean Curvature of Riemannian Foliations

Canadian Mathematical Bulletin, 1996
AbstractIt is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the basic ...
March, Peter, Min-Oo, Maung, Ruh, Ernst A.   +2 more
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Riemannian Mean Curvature Flow

2005
In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local ...
Raúl San José Estépar, Steven Haker, Carl-Fredrik Westin   +2 more
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Linear approximation of mean curvature

2017 IEEE International Conference on Image Processing (ICIP), 2017
Mean curvature has been shown a good regularization for many image processing tasks. Computing mean curvature, however, usually requires the image at least twice differentiable, which is an issue for discrete images, especially at edges. In this paper, we present several linear schemes to approximate the mean curvature of discrete images, based on ...
Yuanhao Gong, Yuan Xie
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Stochastic Motion by Mean Curvature

Archive for Rational Mechanics and Analysis, 1998
The author establishes the existence of a continuously time-varying random subset \(K(t)\) of Euclidean space such that its boundary, which is a hypersurface, has normal velocity formally equal to the mean curvature plus a random driving force. This random force is modelled by a stochastic flow of diffeomorphisms, and the sets \(K(t)\) are sets of ...
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Computing Curvature, Mean Curvature and Weighted Mean Curvature

2022 IEEE International Conference on Image Processing (ICIP), 2022
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Hypersurfaces of Constant Mean Curvature

1989
I want to discuss some aspects of the theory of hypersurfaces of constant mean curvature H. The subject is intimately related to the theory of minimal hypersurfaces which corresponds to the case H = 0. There are, however, some striking differences between the two cases, and this can already be made clear in the simplest situation of surfaces in the ...
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Interfaces of Prescribed Mean Curvature

1987
Several questions of mathematical and physical interest lead to the consideration of an “energy functional” of the following type: $$F[V] = \text{(weighted area of}\, S) + \int_{v}\, H dv,$$ (*) where S is the surface bounding the region V of n-space and H is a given summable function. In the following, we shall be concerned with a problem of
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Nucleation and mean curvature flow

Communications in Partial Differential Equations, 1998
which is written in terms of the characteristic function of the evolving set. The argument is based on implicit time-discretization, derivation of uniform estimates, and passage to thIn this paper ...
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Concentrated Curvature for Mean Curvature Estimation

2010
We present a mathematical result that allows computing the discrete mean curvature of a polygonal surface from the so-called concentrated curvature generally used for Gaussian curvature estimation. Our result adds important value to concentrated curvature as a geometric and metric tool to study accurately the morphology of a surface.
M. M. Mesmoudi, DE FLORIANI, LEILA, MAGILLO, PAOLA   +2 more
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Motion by mean curvature and nucleation

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997
Summary: A model is proposed to represent mean curvature flow (with forcing term), as well as nucleation and other discontinuities in set evolution. A weak formulation in the framework of BV-spaces is written in terms of the characteristic function of the evolving set. This problem has at least one solution.
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