A discretization method for the numerical solution of Dieudonné–Rashevsky type problems with application to edge detection within noisy image data
A discretization method for the numerical solution of Dieudonné–Rashevsky type problems with application to edge detection within noisy image data
复制标题
Dieudonné–Rashevsky 型问题数值解的离散化方法及其在噪声图像数据中边缘检测的应用
DOI：
10.1002/oca.996
复制
发表时间：
2012
影响因子：
1.8
通讯作者：
M. Wagner
中科院分区：
文献类型：
--
作者：
Lucas Franek;Marzena Franek;H. Maurer;M. Wagner
本文研究了用离散化方法和大规模优化技术求解Dieudonné-Rashevsky型多维控制问题。我们首先证明了一个收敛定理，其中的差异的最小值和目标值沿着最小化序列估计的网格大小的基础三角剖分。然后，我们将所提出的方法应用到原始图像数据的边缘检测问题。而不是使用Ambrosio-Tortorelli型能量泛函，我们重新制定的问题作为一个多维控制问题。边缘检测器可以立即从控制变量构建。我们的数值结果的质量竞争以及通过应用变分技术得到的。版权所有© 2011约翰威利父子有限公司.
The present paper is concerned with the numerical solution of multidimensional control problems of Dieudonné–Rashevsky type by discretization methods and large‐scale optimization techniques. We prove first a convergence theorem wherein the difference of the minimal value and the objective values along a minimizing sequence is estimated by the mesh size of the underlying triangulations. Then we apply the proposed method to the problem of edge detection within raw image data. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the problem as a multidimensional control problem. The edge detector can be built immediately from the control variables. The quality of our numerical results competes well with those obtained by applying variational techniques. Copyright © 2011 John Wiley & Sons, Ltd.