图像分割是图像处理和计算机视图中的一项基本任务，它被广泛应用在图像分析、模式识别、物体检测和医学影像等方面。活动轮廓模型已发展成为最成功的图像分割方法之一。传统活动轮廓模型有一些比较好的实验结果，但也有各自的局限性。另外，非凸性是这些模型的一个共同缺点。非凸性不仅会影响分割结果的准确性，也会降低分割的速度或者效率。最近几年Split Bregman方法已被用于更有效地解决图像分割问题。本项目通过将全局凸分割方法的思想应用于传统活动轮廓模型，建立几个全局极小或凸的活动轮廓模型来保证分割结果的准确性与鲁棒性。新模型能量泛函的特殊结构使得可以应用Split Bregman方法快速极小化它，保证新模型可以更快速地分割图像。新模型相比原有模型的优越性主要体现在分割结果的准确性、算法收敛的快速性以及对噪声的鲁棒性等方面。本项目的研究在医学领域中断层扫描以及核磁共振图像分析与处理中具有广阔应用前景。

Image segmentation is a fundamental task in image processing and computer vision, and it is widely applied in image analysis, pattern recognition, object detection, and medical imaging. Active contour models have become one of the most successful methods for image segmentation. Although traditional active contour models can get good numerical and experimental results, they all have their own limitations. Besides, non-convexity is the common disadvantage of these models. Non-convexity can not only affect the accuracy of segmentation results, but also decrease the segmentation speed or efficiency. Recently, the Split Bregman method has been applied to solve image segmentation problems more efficiently. In this project, we will establish several globally convex active contour models to guarantee the accuracy and robustness of segmentation results by applying the idea of the globally convex segmentation method to traditional active contour models. The special structure of the proposed energy functionals guarantees that we can apply the Split Bregman method to fast minimize them, which ensures that the new models can segment images much more efficiently. Compared with original models, the main advantages of the new models are the accuracy of segmentation results, the efficiency of algorithms, the robustness to noise, and so on. Research of this project has extensive application foreground in image analysis and process of computed tomography and magnetic resonance images in medicine area.