Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution
It offers an efficient computational approach for PDE-based colour image segmentation, but the method is incremental as it combines existing models with a multigrid solver.
The paper proposes a multigrid-based numerical method for solving the vector-valued Allen-Cahn phase-field model for colour image segmentation, demonstrating efficient and robust segmentation of large images.
We propose a new method for the numerical solution of a PDE-driven model for colour image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms. This method is known to be closely related to the Mumford-Shah problem and the level set segmentation by Chan and Vese. Our numerical solution is performed using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images.