Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator

TL;DR

This paper introduces a novel two-phase image segmentation method combining a nonlocal edge detection operator with the Allen-Cahn equation, employing efficient numerical schemes and proving their stability and effectiveness.

Contribution

It presents a new nonlocal edge detection technique and integrates it with the Allen-Cahn equation for improved image segmentation, with proven stability and efficiency.

Findings

Effective edge detection using nonlocal Laplacian operator

Stable and energy-preserving numerical schemes

Successful segmentation across various grayscale images

Abstract

Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge detection. The nonlocal edge detection method is used as an initialization for solving the Allen-Cahn equation to achieve two-phase segmentation of the grayscale image. Efficient exponential time differencing (ETD) solvers are employed in the time integration, and finite difference method is adopted in space discretization. The maximum bound principle and energy stability of the proposed numerical schemes are proved. The capability of our segmentation method has been verified in numerical experiments for different types of grayscale images.