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中文摘要：
Potts模型是一种通用的多相图像分割的变分模型,其极值问题需要迭代求解一系列偏微分方程。针对其求解过程计算效率较低的问题,提出一种基于对偶方法的快速算法。采用离散二值标记函数作为特征函数,利用Lagrange乘子法把对特征函数的约束加入能量泛函,然后引入对偶变量改写模型中的长度项,利用KKT的条件得到特征函数的二值解以及对偶变量的简单迭代格式。通过数值实验将该方法与梯度降方法、对偶方法和Split Bregman方法进行比较。实验结果表明,该算法的计算效率和分割准确性都高于其他三种方法。
英文摘要：
Potts model is a general variational model for multiphase image segmentation. Its extremum solution is achieved by solving a series of partial differential equations with iteration, which is of low computation efficiency. To address this problem, we propose a dual method-based fast algorithm. Using several discrete binary labelling functions as characteristic functions, the algorithm puts the constraint of characteristic functions into the energy function with Lagrange multiplier method. Then some dual variables are introduced to reformulate the length item of the model. Finally the binary results of characteristic functions and the simple iterative format of dual variables can be obtained by using KKT （Karush-Kuhn-Tucker） condition. The proposed method is compared with the gradient descent method, dual method and Split Bregman method according to some numerical experiments. Experimental results show that the improved dual method has higher performance in computational efficiency and segmentation accuracy than the other three methods.
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