Convergence of nonlocal geometric flows to anisotropic mean curvature motion

Convergence of an algorithm for anisotropic mean curvature motion

We give a simple proof of convergence of the anisotropic variant of a wellknown algorithm for mean curvature motion, introduced in 1992 by Merriman, Bence and Osher. The algorithm consists in alternating the resolution of the (anisotropic) heat equation, with initial datum the characteristic function of the evolving set, and a thresholding at level 1/2.

Contour Parametrization via Anisotropic Mean Curvature Flows

We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as background. We include a stability criteria for our numerical approximation.

Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

In this paper we prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. This is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, that arises in the theory of dislocations dynamics. We show that if a mean curvature motion is approximated by this type of equations then it is always of variati...

Nonlocal Curvature Flows

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible ge...

Modified Mean Curvature Motion For Multispectral Anisotropic Diffusion