The Weighted Curvature Flow for Planar Curves

• Main Authors: Ying-Jen Lin, 林盈甄
• Other Authors: Jyh-Yang Wu
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/69338041540084300516

博士 === 國立中正大學 === 數學所 === 97 === In this paper we shall discuss a weighted curvature flow for a regular curve in R2. The weighted curvature flow for the planar curves is a generalization of the well-known curvature flow discussed by M. Gage and R. S. Hamilton . Under the suitable weighted curvature flow, convex curves will remain convex under the deformation process; moreover, it still remains embedded if the initial curve is embedded. However, the curve may not converge to a round point for general weights. Indeed, for a nonnegative weight function !(u) with n isolated zeros, a curve will converge to a limiting n-polygon. The weighted curvature flow will have many useful properties which have applications to image processing as the usual curvature flow does.