Diffeomorphic image matching with left-invariant metrics
Diffeomorphic image matching with left-invariant metrics
复制标题
具有左不变度量的微分同胚图像匹配
DOI：
10.1007/978-1-4939-2441-7_16
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Franccois
中科院分区：
文献类型：
--
作者：
T. Schmah;L. Risser;Franccois
通过微分度量映射（LDDMM）进行大变形的微分图像配准的几何方法是基于图像上的微分同构的左作用和微分同构群上的右不变度量，通常使用再现核来定义。我们探索在差分同构群上使用左不变度量，基于在源图像的体坐标中定义的复制核。这种视角，我们称之为左- ldm，允许我们考虑非各向同性的空间变化核，它可以被解释为描述源图像的可变可变形性。我们还展示了LDDMM和新方法之间的简单关系，这意味着在LDDMM中可以以相同的方式解释空间变化的核。最后，我们讨论了一类强制软镜像对称约束的核，我们在一个受损大脑模型上的数值实验中验证了这一点。
The geometric approach to diffeomorphic image registration known as large deformation by diffeomorphic metric mapping (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant metrics on diffeomorphism groups, based on reproducing kernels defined in the body coordinates of a source image. This perspective, which we call Left-LDM, allows us to consider non-isotropic spatially-varying kernels, which can be interpreted as describing variable deformability of the source image. We also show a simple relationship between LDDMM and the new approach, implying that spatially-varying kernels are interpretable in the same way in LDDMM. We conclude with a discussion of a class of kernels that enforce a soft mirror-symmetry constraint, which we validate in numerical experiments on a model of a lesioned brain.