论文信息 - Riemannian Mean Curvature Flow

Riemannian Mean Curvature Flow

In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local structure tensor. Examples on both synthetic and real data are shown.

Carl-Fredrik Westin | Raúl San José Estépar | Steven Haker

[1] P. Olver,et al. Conformal curvature flows: From phase transitions to active vision , 1996, ICCV 1995.

[2] T. Ilmanen. Generalized flow of sets by mean curvature on a manifold , 1992 .

[3] Guillermo Sapiro,et al. Geodesic Active Contours , 1995, International Journal of Computer Vision.

[4] J. Sethian,et al. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[5] Yun-Gang Chen,et al. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations , 1989 .

[6] M. Grayson. The heat equation shrinks embedded plane curves to round points , 1987 .

[7] I. Holopainen. Riemannian Geometry , 1927, Nature.

[8] S. Osher,et al. Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[9] A. Sarti,et al. Subjective surfaces and Riemannian mean curvature flow of graphs. , 2001 .

[10] M. Gage,et al. The heat equation shrinking convex plane curves , 1986 .

[11] L. Evans,et al. Motion of level sets by mean curvature. II , 1992 .