改进的Mumford-Shah模型及其在图像恢复和分割中的应用  

The Reduced Mumford-Shah Model and Its Applications in Image Recovery and Segmentation

作　　者：毕翔[1] 豆泽阳 李浩[1] 

机构地区：[1]中国传媒大学理学院,北京100024

出　　处：《中国传媒大学学报（自然科学版）》2015年第2期39-46,53,共9页Journal of Communication University of China：Science and Technology

摘　　要：在本文中,我们讨论了几个在图像恢复和图像分割中的经典泛函,并且我们用非凸泛函去近似它们。这些经典泛函和两个变量相关u、v,其中u是图像本身,v是它的边缘。这样的话,这个问题就包含着两个方程和两个未知变量,而在我们的近似非凸泛函中,只需要解关于u的一个单变量系统,因为我们引入了趋近于0的参数ρ,把v表示成了一个关于u的梯度的函数。我们还讨论了这些近似模型关于时间的演化方程。最后,在我们的数值实验中,计算了p=1的情况。我们发现算法不但很快,而且也可以很好地保留边缘。In this paper,we discuss several classical functionals in image recovery and segmentation. Mo-reover,we approximate them by nonconvex functional. These classical functionals are related to two varia-bles u and v ,where u is the image function and v is another variable which allows to detect the contours. Then this question consists in two equations and two unknowns,while in our approximate nonconvex func-tional,we only need to solve a system about one variable u. Because we introduce a parameter ρ,which goes to zero. Then we could express v as a function of the gradient of u . We also discuss the evolution e-quation of these models about time. Finally, in our numerical experiment, we compute the model in the case p=1 and find that not only the algorithms are faster but also the edges are very-well preserved.

关 键 词：图像恢复和分割 偏微分方程 欧拉方程 非凸泛函 

分 类 号：O241.82[理学—计算数学]