Numerical methods for motion of level sets by affine curvature

We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite difference schemes, using the theory of viscosity solutions. We demonstrate that our approximate solutions capture the affine invariance and morphological properties of the evolution. Numerical experiments demonstrate the accuracy and stability of the discretization.