Iterative Multigrid Regularization Techniques for Image Matching
Iterative Multigrid Regularization Techniques for Image Matching
复制标题
图像匹配的迭代多重网格正则化技术
DOI：
10.1137/s106482750037161x
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
K. Witsch
中科院分区：
文献类型：
--
作者：
S. Henn;K. Witsch
在本文中，我们考虑了图像匹配问题，即找到一个形变u，它将一幅数字图像变换成另一幅数字图像，使得图像在每个图像元素中具有几乎相等的灰度值。两幅图像的差异是通过它们的L2差异来衡量的，应该最小化。这对u产生了一个非线性病态反问题，因此数值解是相当困难的。考虑了一种Tikhonov正则化方法来排除最小化问题的间断和不规则解。一个重要的问题是正则化参数$\α$的适当选择。对于$α的实际选择，我们采用了基于多重网格技术的迭代正则化方法。为了获得合适的初始猜测，我们使用了一种类似于Brandt[Math]开发的完全多重网格(FMG)的方法。比较，31(1977)，第333--390页]。该算法具有最佳的复杂性：工作量与图像元素的数量成正比。最后，我们给出了一些合成图像和真实图像的实验结果。
In this paper, we consider the problem of matching images, i.e., to find a deformation u, which transforms a digital image into another such that the images have nearly equal gray values in every image element. The difference of the two images is measured by their L2-difference, which should be minimized. This yields a nonlinear ill conditioned inverse problem for u, so the numerical solution is quite difficult. A Tikhonov regularization method is considered to rule out discontinuous and irregular solutions to the minimization problem. An important problem is a proper choice of the regularization parameter $\alpha$. For the practical choice of $\alpha,$ we use iterative regularization methods based on multigrid techniques. To obtain a suitable initial guess, we use an approach similar to the full multigrid (FMG) developed by Brandt [Math. Comp., 31 (1977), pp. 333--390]. The algorithms have optimal complexity: the amount of work is proportional to the number of picture elements. Finally, we present some experimental results for synthetic and real images.