中文摘要：

近年来变分水平集方法在图像分割中得到了广泛应用,但此类方法的能量泛函是非凸的,易陷入局部极小值解。本文基于AA（Aubert-Aujol）去噪模型和变分水平集方法,提出一个局部统计活动轮廓模型,通过凸松弛技术将提出的分割模型转换成全局优化模型,再加入一个迫近算子项,将提出的模型转化为ROF去噪模型,最后采用快速去噪算法,得到一个全局最优的快速分割算法。此算法不涉及差分或微分方程,只需要简单的差分运算,提高了数值运算速度。对实测SAR图像进行分割实验,结果表明,本文提出的全局分割模型不但能够快速、有效地分割SAR图像,取得全局最小值,而且可以更准确地得到图像分割边缘。

英文摘要：

Recently, variational level set method is widely used in image segmentation, but its energy functional is non-convex, which can easily get stuck in local minima. Firstly, we propose a locally statistical active contour model （LACM）based on Aubert-Aujol （AA） denolsing model and variational level set method. Secondly, we transform the proposed model into a global optimization model by u- sing convex relaxation technique~ Thirdly, we add the proximal function to transform the global opti- mization model to a ROF denoising model. Finally, by using a fast denoising algorithm, we obtain a fast segmentation algorithm with global optimization solver, which does not involve partial differential equation or difference equation, and only need simple difference computation. The algorithm can re- duce the running time. By segmenting SAR images, the proposed globally segmentation model not on- ly can detect boundaries of images robustly and efficiently, and obtain a stationary global minimum, but also get the image segmentation boundary more accurately.