多相图像分割的变分模型采用水平集函数定义不同区域的特征函数,其极值问题需要迭代求解一系列动态演化方程,计算效率低。较快的方法是对离散的二值标记函数凸松弛后设计对偶方法或Split Bregman方法,并结合阈值化技术得到分割结果。提出一种无需凸松弛和阈值化的快速分割方法—直接对偶方法(DDM)。DDM利用二值标记函数的二值特性,并根据KKT条件得到原变量的二值解析解和对偶变量的简单迭代格式。该方法首先应用到两相Chan-Vese模型,然后拓展到多相Chan-Vese模型。实验结果表明,DDM比梯度降方法、对偶方法和Split Bregman方法分割效果好、计算效率高。

The multiphase image segmentation is modeled as a minimization problem with characteristic functions defined by level set functions, which leads to solutions of some gradient descent equations with low computation efficiency. This is improved via the dual method or Split-Bregman method using binary labeling functions and convex relaxation, thresholding techniques. In this paper, we propose a fast direct dual method (DDM) without convex relaxation and thresholding techniques. First, we design the DDM for the two-phase Chan-Vese model, which results in a binary solution of the primal variable in analytical form and a simple iterative formulation of the dual variable by using KKT (Karush-Kuhn-Tucker) conditions. Then, it is extended to the Chan-Vese model for multiphase image segmentation. The experimental results demonstrate that the proposed method has a better performance, and is more efficient than the gradient descent method, the dual method, and the Split-Bregman method.