Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

TL;DR

This paper introduces a multigrid finite element method for efficiently solving a PDE-based vector-valued Allen-Cahn model for color image segmentation, demonstrating robustness and effectiveness on large images.

Contribution

It presents a novel multigrid splitting approach for the Allen-Cahn phase-field model tailored to color image segmentation, enhancing computational efficiency and robustness.

Findings

Effective segmentation of large color images

Robust multigrid finite element implementation

Close relation to Mumford-Shah and Chan-Vese models

Abstract

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.