Towards fast non-rigid registration
Towards fast non-rigid registration
复制标题
迈向快速非刚性注册
DOI：
10.1090/conm/313/05369
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发表时间：
2003
影响因子：
0.7
通讯作者：
M. Rumpf
中科院分区：
文献类型：
--
作者：
U. Clarenz;M. Droske;M. Rumpf
提出了一种用于 2D 和 3D 图像匹配的快速多尺度和多重网格方法。特别是在医学成像中，被称为配准问题的这个问题在处理来自多个图像模态或图像时间序列的图像时具有根本重要性。论文限制了最简单的匹配能量最小化，即 A.AE C:E±E¶E EI`I3I I E Ð C#N I E I E ，其中 I E 、 I E 是要匹配的两个图像的强度图，C 是变形。重点是稳健且高效的解决方案策略。图像匹配，即找到最小化 A 的最佳变形 C，已知是一个不适定问题。因此，为了规范这个问题，在梯度流方法中考虑下降路径的正则化。因此，具有一些规则初始变形 Cu×UOGUSECU 的初始值问题 O>O CHE¤N grad OOA.AE COE 在适当的变形空间 UÝØU 上求解。梯度梯度 O 是通过 w.r.t → 合适的正则化度量 s 来测量的。对于不同类型的正则化，证明了解的存在性和唯一性。为了实现，提出了一种基于分层网格上的多重网格循环的度量，利用其优越的平滑特性。这与下降算法中的有效时间步长控制相结合。此外，为了避免收敛到局部最小值，考虑了要匹配的图像的多个尺度。同样，这些图像比例可以使用多重网格算子生成，我们建议在正确选择的分层网格金字塔上解析比例金字塔。 2D 和大型 3D 图像匹配问题的示例证明了所提出方法的鲁棒性和效率。
A fast multiscale and multigrid method for the matching of images in 2D and 3D is presented. Especially in medical imaging this problem denoted as the registration problem is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper restricts to the simplest matching energy to be minimized, i.e., A.AE C:E±E¶E EI`I3I I E Ð C#N I E I E , where I E , I E are the intensity maps of the two images to be matched and C is a deformation. The focus is on a robust and efficient solution strategy. Matching of images, i.e., finding an optimal deformation C which minimizes A is known to be an ill-posed problem. Hence, to regularize this problem a regularization of the descent path is considered in a gradient flow method. Thus the initial value problem O>O CHE¤N grad OOA.AE COE with some regular initial deformation Cu×UOGUSECU is solved on a suitable space of deformations UݬU . The gradient grad O is measured w.r.t Þ a suitable regularizing metric s . Existence and uniqueness of solutions is demonstrated for different types of regularizations. For the implementation a metric based on multigrid cycles on hierarchical grids is proposed, using their superior smoothing properties. This is combined with an effective time-step control in the descent algorithm. Furthermore, to avoid convergence to local minima, multiple scales of the images to be matched are considered. Again, these image scales can be generated applying multigrid operators and we propose to resolve the pyramid of scales on a properly chosen pyramid of hierarchical grids. Examples on 2D and large 3D image matching problems prove the robustness and efficiency of the proposed approach.