Level Set Method Based on Molecular Beam Epitaxy Equation for Image Segmentation

Image segmentation is an important and complex task in computer vision. The variational level set method has become a popular approach for image segmentation due to its topological invariance. However, the evolution process may be unstable, leading to segmentation failures due to excessively flat or sharp final evolutionary profiles. In order to improve the accuracy and stability of evolution, we propose a high-order level set variational model, which applies the variational form of the molecular beam epitaxy (MBE) equation. The model avoids the need for re-initialization. In order to calculate the model, we drive the gradient flow of the model. We propose a finite difference semi-implicit and semi-explicit scheme. Additionally, we also design the scalar auxiliary variable scheme of the model, which expands its application, and can be solved by fast algorithms. Numerical experiments show that the model is outperforms current mainstream models in the processing of noisy images and medical images, and can be applied to actual image segmentation problems.