We present a new numerical scheme for planar curve evolution with a normal velocity equal to F (k), where k is the curvature and F is a nondecreasing function such that F (0) = 0 and either x bar right arrow F (x(3)) is Lipschitz with Lipschitz constant less than or equal to 1 or F (x) = x(gamma) for gamma greater than or equal to 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. [References: 30]
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