论文标题
艾伦（Allen）的多相图像分割 - -cahn chan - vese模型
Multi-phase image segmentation by the Allen--Cahn Chan--Vese model
论文作者
论文摘要
本文提出了一个Allen-Cahn Chan-Vese模型来解决多相图像分割。我们首先整合了allen-cahn项和chan - vese拟合能量项，以建立一个能量功能，该功能的最小值定位了分割轮廓。随后的最小化过程可以归因于拟合强度的变异计算以及几个allen-cahn方程的解决方案近似，其中$ n $ n $ allen-cahn方程足以分区$ m = 2^n $段。派生的allen-cahn方程是通过具有指数时间集成和有限差空间离散化的有效数值求解器来求解的。证明了所提出的数值方案的离散最大结合原理和能量稳定性。最后，在各种实验中验证了不同类型的图像的分割方法的能力。
This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to establish an energy functional, whose minimum locates the segmentation contour. The subsequent minimization process can be attributed to variational calculation on fitting intensities and the solution approximation of several Allen-Cahn equations, wherein $n$ Allen-Cahn equations are enough to partition $m = 2^n$ segments. The derived Allen-Cahn equations are solved by efficient numerical solvers with exponential time integrations and finite difference space discretization. The discrete maximum bound principle and energy stability of the proposed numerical schemes are proved. Finally, the capability of our segmentation method is verified in various experiments for different types of images.
