Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631435 | Applied Mathematics and Computation | 2010 | 21 Pages |
Abstract
In this paper we shall discuss a weighted curvature flow for a regular curve in the 2D Euclidean space. The weighted curvature flow for planar curves is a generalization of the well-known curvature flow discussed by Gage, Hamilton and Grayson. Under a suitable weighted curvature flow, convex curves will remain convex in the deformation process. However, the curve may not converge to a round point for general weights. Indeed, for a nonnegative weight function Ï(u) with k isolated zeros, a curve will converge to a limiting k-polygon. The weighted curvature flow will have many useful properties which have applications to image processing. We shall also present some numerical simulations to illustrate how curves deform under the weighted curvature flow with different weight functions Ï(u). Moreover, our algorithm is very effective and stable. The approximation of higher derivatives in our new algorithm only involve in the neighboring points.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sheng-Gwo Chen, Mei-Hsiu Chi, Ying-Jen Lin, Jyh-Yang Wu,