一种基于拓扑渐进展开的边缘检测方法
n approach to edge detection by topological asymptotic analysis
在本文中，在未知先验信息的情况下，用一种变分的方法对图像进行边缘检测。首先，基于Mumford-Shah函数最小化定义一函数并推导出此函数的渐进拓扑展开公式。然后，证明图像最优的边界集是满足下面两个条件的点集：（一）定义函数渐进展开的最主要项取值最小；（二）定义函数拓扑导数为零 。根据上面两个条件就可以进行边缘检测，无需对参数事先设定。最后，利用数值实验证明了此方法的可行性。
In this paper，we use a variational approach to the problem o f edge detection without any priori information. At first, based on the theory of Mumford-Shah functional minimum, we define a function and derive its topological asymptotic analysis. Secondly, we proof the optimal edge sets must satisfy the following condtions: the dominant term of this expansion is minimal and the topological graditude is equal to zero. At last,we use the numerical experiments to illustrate this method.
杜朝晖、潘文峰
计算技术、计算机技术
拓扑渐进分析自由参数边缘检测M-S函数
opological asymptotic analysisparameter-free edge detectionMumford-Shah function
杜朝晖,潘文峰.一种基于拓扑渐进展开的边缘检测方法[EB/OL].(2012-11-21)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/201211-380.点此复制
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