Threshold dynamics for high order geometric motions

  • Selim Esedoglu

    University of Michigan, Ann Arbor, United States
  • Steven J. Ruuth

    Simon Fraser University, Burnaby, Canada
  • Richard Tsai

    University of Texas at Austin, United States


In this paper, a class of algorithms for the high order geometric motion of planar curves is developed. The algorithms alternate two simple steps—a convolution and a thresholding step—to evolve planar curves according to combinations of Willmore flow, surface diffusion flow and curvature motion. A distinguishing feature of the methods is that they posses much better stability than typical explicit algorithms. Formal expansions and numerical examples are provided for a variety of high order flows to validate the methods and illustrate their behaviors.

Cite this article

Selim Esedoglu, Steven J. Ruuth, Richard Tsai, Threshold dynamics for high order geometric motions. Interfaces Free Bound. 10 (2008), no. 3, pp. 263–282

DOI 10.4171/IFB/189