Solution of nonlinearly curvature driven evolution of plane curves Original Research Article

The evolution of plane curves obeying the equation v=β(k), where v is normal velocity and k curvature of the curve is studied. Morphological image and shape multiscale analysis of Alvarez, Guichard, Lions and Morel and affine invariant scale space of curves introduced by Sapiro and Tannenbaum as well as isotropic motions of plane phase interfaces studied by Angenent and Gurtin are included in the model. We introduce and analyze a numerical scheme for solving the governing equation and present numerical experiments.