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.
Cite
@article{arxiv.0710.0736,
title = {Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution},
author = {David A Kay and Alessandro Tomasi},
journal= {arXiv preprint arXiv:0710.0736},
year = {2018}
}