Multi-phase image segmentation by the Allen--Cahn Chan--Vese model

TL;DR

This paper introduces a novel multi-phase image segmentation method combining Allen-Cahn and Chan-Vese models, using efficient numerical schemes to accurately partition images into multiple segments.

Contribution

It develops an integrated energy functional and efficient numerical algorithms for multi-phase segmentation, enabling accurate partitioning into multiple regions.

Findings

Effective segmentation of various image types.

Numerical schemes with proven stability and efficiency.

Capable of partitioning into multiple segments with fewer equations.

Abstract

This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to establish an energy functional, whose minimum locates the segmentation contour. The subsequent minimization process can be attributed to variational calculation on fitting intensities and the solution approximation of several Allen-Cahn equations, wherein $n$ Allen-Cahn equations are enough to partition $m = 2^n$ segments. The derived Allen-Cahn equations are solved by efficient numerical solvers with exponential time integrations and finite difference space discretization. The discrete maximum bound principle and energy stability of the proposed numerical schemes are proved. Finally, the capability of our segmentation method is verified in various experiments for different types of images.