A PDE based binary image segmentation model using a modified Cahn–Hilliard equation with weaker fidelity parameter (λ) and double well potential has been introduced. The threshold of separation γ is flexibly chosen between 0 and 1. Convexity splitting is used for time discretization and then Fourier-spectral method is used to solve the proposed modified Cahn–Hilliard equation. The proposed model is tested on bio-medical images.