Communications in Mathematical Sciences
Volume 9 (2011)
Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation
Pages: 637 – 662
Numerical methods for planar anisotropic mean curvature flow are presented for smooth and crystalline anisotropies. The methods exploit the variational level-set formulation of A. Chambolle, in conjunction with the split Bregman algorithm (equivalent to the augmented Lagrangian method and the alternating directions method of multipliers). This induces a decoupling of the anisotropy, resulting in a linear elliptic PDE and a generalized shrinkage (soft thresholding) problem. In the crystalline anisotropy case, an explicit formula for the shrinkage problem is derived. In the smooth anisotropy case, a system of nonlinear evolution equations, called inverse scale space flow, is solved. Numerical results are presented.
Anisotropic mean curvature flow, Wulff shapes, total variation minimization, split Bregman method, shrinkage, soft thresholding, inverse scale space
2010 Mathematics Subject Classification
35K55, 35K65, 49M25, 65K10, 65M06, 65M12