Threshold dynamics for high order geometric motions
Selim Esedoḡlu, Steven J. Ruuth, Richard Tzong‐Han Tsai · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2008
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.