中文摘要：

为降低噪声对图像分割的影响，提出一个几何活动轮廓模型，并应用变分方法求解出模型对应的水平集曲线演化的偏微分方程．该模型考虑到图像区域和边缘的先验信息，并充分考虑图像的统计信息．引入一个惩罚项作为内部能量项，以避免耗时的重新初始化过程．为了验证模型的有效性，文中基于简单的高斯型概率密度函数建立分割实例，结合应用高效且无条件稳定的AOS算法进行分割实验．实验结果表明，模型准确性较高，具有良好的抗噪性、高效性．

英文摘要：

A geometric active contour model is proposed to reduce the influence of noise on image segmentation. The corresponding partial differential equations evolved by the level set curve are got through variational principle. Prior information of the regions and boundaries of the image is considered in this model and the statistical information of the image is considered as well. Moreover, a penalized term is used as an internal energy term to avoid the time-consuming re-initialization process. To verify the efficiency of the proposed model, a segmentation instance based on simple Gauss probability density function is given, and the additive operator splitting （AOS） scheme which is efficient and unconditionally stable is employed. Experimental results show that the proposed model has high accuracy, efficiency and noisy resistance.