Multiphase image segmentation using a phase-field model

In this paper, we propose a new, fast, and stable hybrid numerical method for multiphase image segmentation using a phase-field model. The proposed model is based on the Allen-Cahn equation with a multiple well potential and a data-fitting term. The model is computationally superior to the previous multiphase image segmentation via Modica-Mortola phase transition and a fitting term. We split its numerical solution algorithm into linear and a nonlinear equations. The linear equation is discretized using an implicit scheme and the resulting discrete system of equations is solved by a fast numerical method such as a multigrid method. The nonlinear equation is solved analytically due to the availability of a closed-form solution. We also propose an initialization algorithm based on the target objects for the fast image segmentation. Finally, various numerical experiments on real and synthetic images with noises are presented to demonstrate the efficiency and robustness of the proposed model and the numerical method.