منابع مشابه
Motion of Level Sets by Mean Curvature. I
We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γo a unique generalized motion by mean curvature, existing for all time. We investigate the various geometric properties and pathologies of this evolution.
متن کاملMotion of Level Sets by Mean Curvature. Ii
We give a new proof of short time existence for the classical motion by mean curvature of a smooth hypersurface. Our method consists in studying a fully nonlinear uniformly parabolic equation satisfied by the signed distance function to the surface
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We propose a finite element algorithm for computing the motion of a surface moving by mean curvature. The algorithm uses the level set formulation, so that changes in topology of the surface can be accommodated. Stability is deduced by showing that the discrete solutions satisfy both L°° and W' bounds. Existence of discrete solutions and connections with Brakke flows are established. Some numer...
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This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. After brieey presenting an axiomatic approach of image processing and the mean curvature PDE, the properties of the proposed scheme are studied, in particular consistency and convergence are proved. The applications of mean curvature motion in image denoising and form evolution are...
متن کاملMotion of Level Set by General Curvature
In this paper, we study the motion of level sets by general curvature. The difficulty in this setting is for a general curvature function, it’s only well defined in an admissible cone. In order to extend the existence result to outside the cone we introduce a new approximation function f̂ (see (3.1)). Moreover, using the idea in [5], we give an elliptic approach for the Ben-Andrews’ non-collapsi...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 1995
ISSN: 1050-6926,1559-002X
DOI: 10.1007/bf02926443