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Threshold dynamics for high order geometric motions. (English) Zbl 1157.65330
Summary: 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.

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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