Expanding selfsimilar solutions of a crystalline flowwith applications to contour figure analysis

Hidekata Hontani, Mi-Ho Giga, Yoshikazu Giga, Koichiro Deguch

Abstract: A numerical method for obtaining a crystalline flow starting from a general polygon is presented.Acrystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvatureflow. In some cases, new facets may be created instantaneously and their facet lengths are governedby a system of singular ordinary differential equations (ODEs). The proposed method solves thesystem of the ODEs numerically by using expanding selfsimilar solutions for newly created facets.The computation method is applied to a multi-scale analysis of a contour figure.© 2004 Elsevier B.V. All rights reserved.