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中文摘要：
针对隐式曲面上多相图像分割的问题，基于曲面的隐式表达、隐式曲面上的内蕴梯度等概念，将用于平面图像分割的Potts模型推广。首先对于隐式封闭曲面和隐式开放曲面，分别给出Potts模型的推广形式。然后对于传统梯度降方法计算效率低的问题，为曲面上的Potts模型设计了Split Bregman算法和对偶方法，并在对偶方法的基础上提出了一种改进的快速算法。多个数值实验结果表明，所提出的曲面上的Potts模型能有效地分割闭／开曲面上的分段常值图像，并且新的改进对偶方法在计算效率方面优于其他两种方法。
英文摘要：
With the use of implicit expression of surfaces and intrinsic gradient, this paper extended the Potts model for planar image segmentation to variational models for image segmentation on implicit surfaces. It formulated the corresponding Potts models both on implicit closed surfaces and on implicit open surfaces. To obtain higher computational efficiency, it did not em- ploy traditional gradient descent method. Instead, it designed Split Bregman method and dual method for the generalized Potts model. Furthermore, it proposed an improved dual method. Some numerical experiments show that the proposed Potts models on implicit surfaces can segment piecewise constant images on surfaces effectively. And the improved dual method is superior to Split Bregman method and dual method in computational efficiency.
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