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Medientyp:
E-Artikel
Titel:
Geometric Computation of Curvature Driven Plane Curve Evolutions
Beteiligte:
Cao, Frédéric;
Moisan, Lionel
Erschienen:
Society for Industrial and Applied Mathematics, 2002
Erschienen in:SIAM Journal on Numerical Analysis
Sprache:
Englisch
ISSN:
0036-1429
Entstehung:
Anmerkungen:
Beschreibung:
<p> We present a new numerical scheme for planar curve evolution with a normal velocity equal to F(κ), where κ is the curvature and F is a nondecreasing function such that F(0) = 0 and either x → F(x<sup>3</sup>) is Lipschitz with Lipschitz constant less than or equal to 1 or F(x) = x<sup>γ</sup> for γ ≥ 1/3. The scheme is completely geometrical and avoids some drawbacks of finite difference schemes. In particular, no special parameterization is needed and the scheme is monotone (that is, if a curve initially surrounds another one, then this remains true during their evolution), which guarantees numerical stability. We prove consistency and convergence of this scheme in a weak sense. Finally, we display some numerical experiments on synthetic and real data. </p>