Geometric Invariant Shape Representations Using Morphological Multiscale Analysis
Journal of Mathematical Imaging and Vision
| Hi-index | 0.00 |
We present a new numerical scheme for planar curve evolution with a normal velocity equal to $F(\kappa)$, where $\kappa$ is the curvature and F is a nondecreasing function such that F(0)=0 and either $x\mapsto F(x^3)$ is Lipschitz with Lipschitz constant less than or equal to 1 or $F(x)=x^\gamma$ for $\gamma\geq 1/3$. 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.