• 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
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  • 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&lt;sup&gt;3&lt;/sup&gt;) is Lipschitz with Lipschitz constant less than or equal to 1 or F(x) = x&lt;sup&gt;γ&lt;/sup&gt; 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>