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. © 2011 International Press.
CITATION STYLE
Oberman, A., Osher, S., Takei, R., & Tsai, R. (2011). Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation. Communications in Mathematical Sciences, 9(3), 637–662. https://doi.org/10.4310/CMS.2011.v9.n3.a1
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