A Phase Field Model for Image Decomposition and Smoothing

In this paper we propose a new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation. The Cahn-Hilliard equation was first formulated as the minimization of a free energy that reflects the topological events, phase coarsening and separation processes. We replaced the energy density in this equation with the derivative of a new convex energy which allows only the decomposition of phase values into multiple layers. This system, although based on a variational formulation does not require the solution of an optimization problem and its main advantage is the flexibility it provides in designing decomposition algorithms. Within this framework, we developed several algorithms based on order statistics for image smoothing and decomposition.