Diffusion generated motion using signed distance functions

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to the interface, and convolution with a suitable kernel. These algorithms can be seen as variants of Merriman, Bence, and Osher’s threshold dynamics [25]. The new algorithms proposed here preserve the computational efficiency of the original threshold dynamics algorithm. However, unlike threshold dynamics, the new algorithms also allow attaining high accuracy on uniform grids, without adaptive refinement.