Algorithms for stochastic approximations of curvature flows

Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work G. Ben-Arous et al. (2002), we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve shortening flows initiated by convex curves. The present note shows that this theory may be implemented as a new way of evolving curves and as a possible alternative to level set methods.