Diffusion generated motion using signed distance functions

  • Authors:

  • Selim Esedoglu;Steven Ruuth;Richard Tsai

  • Affiliations:

  • Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA;Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6;Department of Mathematics, University of Texas, Austin, TX 78712, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

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.