Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

Authors:
Hidekata Hontani;Mi-Ho Giga;Yoshikazu Giga;Koichiro Deguchi
Affiliations:
Department of Informatics, Yamagata University, Yonezawa, Yamagata, 992-8510, Japan;Department of Mathematics, Hokkaido University, Sapporo, Hokkaido, 060-0810, Japan;Department of Mathematics, Hokkaido University, Sapporo, Hokkaido, 060-0810, Japan;Department of System Information Sciences, Graduate School of Tohoku University, Sendai, 980-8579, Japan
Venue:
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Year:
2005

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Abstract

A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system 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.