中文摘要：

针对自然图像中内容的多样性、复杂性以及随机性，若采用区域内部恒定聚类中心假设的cv（chan—Vese）模型以及多类水平集模型，则难以有效刻画具有非线性、连续性变化的自然图像内容。该文通过对区域内部自由度调控的多变量学生．概率密度分布描述，提出了多类非线性变分活动轮廓模型，它打破了区域内部恒定密度的约束。由于多类非线性变分活动轮廓模型缺乏区域外力，容易分割出离散、零碎的噪声区域，通过引入测地线区域外力约束项，能有效分割出区域间的光滑边界。针对多类变分模型的最小化问题枷难问题，提出对多类变分活动轮廓模型进行离散化表达，然后构建对应的多层图割模型，并利用最大流／最小割优化方式快速求得全局近似最优解。实验表明，该文提出的分割方法能够准确地分割出多类非同质目标区域，且区域之间的边界光滑，视觉效果好。

英文摘要：

The content of the natural image is diversity, complexity, and randomly, so that the nonlinear and continuity change of natural image cannot be described effectively by using the constant density assumption of regions in CV （Chan-Vese） model or multiphase level sets model. In this paper, we propose a multi-class nonlinear variational model that can break up the bottleneck of constant density through introducing the multivariable mixed student-t distribution. We further integrate the geodesic active model into the proposed model for getting some smoothly edges between regions. Additionally, the energy minimization of our proposed model is a NP hard problem, but, we can discretize the variational formulation into discretization form, and then find the approximate optimization solution through maximization flow/minimization cuts theory. Lastly, a large number of natural images are adopted for experiment comparison. The segmentation results demonstrate the superiority of our proposed method, such as the effective discriminate ability of multiple non-homogeneous regions, smooth edges, and good visual effect.