Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation

16Citations
Citations of this article
12Readers
Mendeley users who have this article in their library.

Abstract

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.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free