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, and thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve. 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 scalar auxiliary variable (SAV) scheme coupled with fast Fourier transform (FFT), 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, retain fine segmentation targets 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.

翻译：变分水平集方法因其能够处理复杂拓扑变化并在演化过程中保持连续性与平滑性，已成为图像分割领域的有力工具。然而其演化过程可能不稳定，导致轮廓过度平坦或过度锐化，进而造成分割失败。为提高演化的准确性与稳定性，本文提出一种结合分子束外延（MBE）方程正则化的高阶水平集变分分割方法。该方法利用MBE过程中的晶体生长机制约束水平集函数的演化，从而避免演化过程中的重初始化操作，并调控分割曲线的平滑度。该方法同样适用于具有强度不均匀性的噪声图像，这是图像分割中的难点问题。为求解该变分模型，我们推导了梯度流方程，并设计了结合快速傅里叶变换（FFT）的标量辅助变量（SAV）格式，与传统半隐式-半显式格式相比，计算效率显著提升。数值实验表明，所提方法能够生成平滑的分割曲线，保留精细分割目标，并获得小目标的鲁棒分割结果。与现有水平集方法相比，该模型在精度与效率方面均达到先进水平。