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

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Abstract

Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function. Thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve and keep the segmentation results independent of the initial curve selection. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design a scalar auxiliary variable scheme, which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, preserve segmentation details and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (U21B2075), National Key R &D Program of China (2023YFC2205900, 2023YFC2205903), the National Natural Science Foundation of China (12171123, 12271130, 12371419), Natural Sciences Foundation of Heilongjiang Province (ZD2022A001), Self-Planned Task of State Key Laboratory of Robotics and System (HIT) (SKLRS201801A05), the Fundamental Research Funds for the Central Universities (2022FRFK060020, 2022FRFK060014).

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  1. State Key Laboratory of Robotics and System (HIT), School of Mathematics, Harbin Institute of Technology, No. 92 Dazhi Street, Harbin, 150001, China

    Fanghui Song, Jiebao Sun, Shengzhu Shi, Zhichang Guo & Dazhi Zhang

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Song, F., Sun, J., Shi, S. et al. Re-initialization-Free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation. J Math Imaging Vis (2024). https://doi.org/10.1007/s10851-024-01205-x

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