采用迎风格式的水平集算法实现需要在曲线演化过程中重新初始化水平集函数的要求，为保证算法的稳定，时间步长选取较小值，算法运行速度较慢。文中基于无须重新初始化的水平集方法，在算法数值实现中引入AOS半隐格式，对基于不同统计模型的水平集分割算法给出统一的数值实现。以二相水平集分割算法为基础提出一种新的多相水平集分割方法。该方法采用一个水平集函数进行多次演化实现多区域分割，其优点包括：1)采用AOS半隐格式，该格式无条件稳定，可采用较大的时间步长；2)对多个统计模型进行统一处理；3)采用单一的水平集函数进行演化，减少水平集演化方程的数量，算法更加灵活。实验结果表明，该方法具有较快的分割速度，对具有多个区域的图像能够进行较准确的分割。%The numerical implementation of level set method based on upwind scheme needs to reinitialize the level set function during the evolution of the curve. To guarantee the stability of the algorithms, a small time-step must be selected, which slows down the running speed. Based on a level set method without reinitialization, a semi-implicit additive operator splitting ( AOS ) scheme is used in numeri cal implementation, and a unified implementation for different statistical models is provided. Based on two-phase segmentation, a new level set method for multiphase segmentation is proposed. This method uses a unique level set function many times during curve evolution to realize multiregion segmentation. Its advantages are as follows. AOS scheme is used in this method which is unconditionally stable, and it allows to use a large time-step. It provides unified numerical implementation for many kinds of statistical models. The unique level set function is used in curve evolution, which reduces the amount of evolution equations and is more flexible. The experimental results show that the proposed method is more efficient and can segment multiregion images exactly.
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