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. 263–282DOI 10.4171/IFB/189