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Variational level set method has become a powerful tool in image segmentationdue to its ability to handle complex topological changes and maintaincontinuity and smoothness in the process of evolution. However its evolutionprocess can be unstable, which results in over flatted or over sharpenedcontours and segmentation failure. To improve the accuracy and stability ofevolution, we propose a high-order level set variational segmentation methodintegrated with molecular beam epitaxy (MBE) equation regularization. Thismethod uses the crystal growth in the MBE process to limit the evolution of thelevel set function, and thus can avoid the re-initialization in the evolutionprocess and regulate the smoothness of the segmented curve. It also works fornoisy images with intensity inhomogeneity, which is a challenge in imagesegmentation. To solve the variational model, we derive the gradient flow anddesign scalar auxiliary variable (SAV) scheme coupled with fast Fouriertransform (FFT), which can significantly improve the computational efficiencycompared with the traditional semi-implicit and semi-explicit scheme. Numericalexperiments show that the proposed method can generate smooth segmentationcurves, retain fine segmentation targets and obtain robust segmentation resultsof small objects. Compared to existing level set methods, this model isstate-of-the-art in both accuracy and efficiency.

Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation