On a Stochastic Model of Geometric Snakes

Abstract

It this note, we give a formulation of a stochastic snake model based the theory of interacting particle systems and hydrodynamic limits. 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 [71], 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 as a possible alternative to level set methods.