Threshold dynamics for high order geometric motions | Zendy

Selim Esedoḡlu | Zendy; Steven J. Ruuth | Zendy; Richard TzongHan Tsai | Zendy

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Threshold dynamics for high order geometric motions

Author(s) -

Selim Esedoḡlu,

Steven J. Ruuth,

Richard TzongHan Tsai

Publication year - 2008

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/189

Subject(s) - curvature , geometric flow , thresholding , planar , motion (physics) , feature (linguistics) , mathematics , convolution (computer science) , flow (mathematics) , stability (learning theory) , class (philosophy) , surface (topology) , computer science , diffusion , geometry , artificial intelligence , image (mathematics) , physics , linguistics , philosophy , computer graphics (images) , machine learning , artificial neural network , thermodynamics

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 possess 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.

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