Mathematical Models in Computer Vision: 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 \cite{arous-tannenbaum-etal:03}, 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.

	Main		Mathematical Models in Computer Vision: The Handbook, Springer (2005)
	Editors Preface Contents Contributors References Sample Chapter Order		On a Stochastic Model of Geometric Snakes, A. Yezzi, D. Nain, G. Unal, O. Zeitouni and A. Tannenbaum 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 \cite{arous-tannenbaum-etal:03}, 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.

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