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在处理复杂拓扑变化以及保持演化过程连续性和光滑性方面的优势，已成为图像分割的有力工具。然而，其演化过程可能不稳定，导致轮廓过度平坦或过度尖锐，进而引发分割失败。为提高演化的精度和稳定性，我们提出了一种结合分子束外延方程正则化的高阶水平集变分分割方法。该方法利用MBE过程中的晶体生长特性来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，并调节分割曲线的光滑度。该方法同样适用于存在强度不均匀性的噪声图像处理，而这是图像分割中的一个挑战。为求解该变分模型，我们推导了梯度流，并设计了耦合快速傅里叶变换的标量辅助变量格式，与传统半隐式和半显式格式相比，该方法能显著提高计算效率。数值实验表明，所提方法可生成光滑的分割曲线，保留精细分割目标，并获取小目标的鲁棒分割结果。与现有水平集方法相比，该模型在精度和效率两方面均达到了先进水平。