A weighted curvature flow for shape deformation

作者：Chen Sheng Gwo^*; Chi Mei Hsiu; Lin Ying Jen; Wu Jyh Yang

来源：Applied Mathematics and Computation, 2010, 217(5): 2097-2117.

DOI：10.1016/j.amc.2010.07.009

• A weighted curvature flow
• Convex curves
• Regular k-polygons

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 omega(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 omega(u). Moreover, our algorithm is very effective and stable. The approximation of higher derivatives in our new algorithm only involve in the neighboring points.

• 出版日期2010-11-1