Mumford-Shah模型在图像分割中的研究

介绍了图像分割中的Mumford-Shah(MS)模型，提出了一种新的MS模型的数值求解方法。首先在数学上指出了MS泛函弱解在SBV函数空间中的存在性，然后讨论了计算弱解的数值逼近方法。为了得到MS泛函的数值解，首先定义了自适应三角剖分空间上的离散型MS泛函，然后在每次迭代前对有限元网格进行相应的自适应调整，接着采用拟牛顿最小化方法，并通过收敛意义上的离散有限元逼近，得到离散型MS泛函在每次迭代中的最小值。实验结果表明，该方法适合含噪图像的分割，是一种有效的图像分割算法。

Research on the Mumford-Shah Model in Image Segmentation

An effective inpainting algorithm for filling-in of spots and cracks in jacquard images is pro- posed·It first improves the classical Mumford-Shah model by imposing some explicit smooth constraints on the formation of discontinuities·Then, a numerical solution of the improved Mumford-Shah model is implemented by its gradient descent flow which leads to two coupled second order partial differential equations, one for the gray levels and the other for the signature function of discontinuities·Experiments on noisy jacquard images are presented to illustrate the feasibility of the algorithm