An algorithm for 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.

Algorithms for computing motion by mean curvature

We propose a finite element algorithm for computing the motion of a surface moving by mean curvature. The algorithm uses the level set formulation, so that changes in topology of the surface can be accommodated. Stability is deduced by showing that the discrete solutions satisfy both L°° and W' bounds. Existence of discrete solutions and connections with Brakke flows are established. Some numer...

Eecient Algorithms for Diiusion-generated Motion by Mean Curvature

The problem of simulating the motion of evolving surfaces with junctions according to some curvature-dependent speed arises in a number of applications. By alternately diiusing and sharpening characteristic functions for each region, a variety of motions have been obtained which allow for topological mergings and breakings and produce no overlapping regions or vacuums. However, the usual nite d...

Diffusion-Generated Motion by Mean Curvature for Filaments

In previous work, we introduced a simple algorithm for producing motion by mean curvature of a surface, in which the motion is generated by alternately diiusing and renormalizing a characteristic function. This procedure is interesting due to its extreme simplicity, and because it isolates the connection between diiusion and curvature motion. However, it makes sense only for surfaces, i.e. obje...

Modified Mean Curvature Motion For Multispectral Anisotropic Diffusion