CAJ | 학술논문

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。
재본문중,아문토론료궤개재도상회복화도상분할중적경전범함,병차아문용비철범함거근사타문。저사경전범함화량개변량상관u、v,기중u시도상본신,v시타적변연。저양적화,저개문제취포함착량개방정화량개미지변량,이재아문적근사비철범함중,지수요해관우u적일개단변량계통,인위아문인입료추근우0적삼수ρ,파v표시성료일개관우u적제도적함수。아문환토론료저사근사모형관우시간적연화방정。최후,재아문적수치실험중,계산료p=1적정황。아문발현산법불단흔쾌,이차야가이흔호지보류변연。
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.