An Effective Level Set Method With Molecular Beam Epitaxy Regularization for Color-Texture Image Segmentation

In this paper, we propose a novel variational model for color–texture image segmentation by embedding the molecular beam epitaxy (MBE) equation into a multi-cue segmentation (MCS) framework. The MBE equation incorporates a fourth-order diffusion term to smooth high-frequency noise while preserving curvature variations, along with a non-equilibrium term to ensure mass conservation and suppress oscillations, thereby eliminating the need for frequent re-initialization. Inspired by the physical principles of crystal film growth, this approach regulates the level set evolution by controlling thin-film growth dynamics, improving both stability and accuracy. We derive the gradient flow equation of the proposed model and prove the existence of a weak solution using the Galerkin approximation method. To solve the model efficiently, we design an implicit–explicit (IMEX) scheme, and employ an additive operator splitting (AOS) method to obtain the diffusion tensor. Extensive experiments demonstrate that the MBE-MCS model achieves more stable level set evolutions, better preserves fine structural details, and delivers superior segmentation accuracy, even for images with noise, sharp corners, and complex backgrounds.