Elastic Shape Analysis of Surfaces and Images
Elastic Shape Analysis of Surfaces and Images
复制标题
表面和图像的弹性形状分析
DOI：
10.1007/978-3-319-22957-7_12
复制
发表时间：
2016
影响因子：
6.6
通讯作者：
Hamid Laga
中科院分区：
文献类型：
--
作者：
S. Kurtek;Ian H. Jermyn;Q. Xie;E. Klassen;Hamid Laga
我们描述了两个参数化曲面的统计形状分析的黎曼框架。这些方法提供了用于表面形状的配准、比较、变形、平均、统计建模和随机采样的工具。这两个框架的一个重要特性是它们对曲面的重新参数化是不变的。因此，它们导致自然形状比较和统计。我们描述的第一种方法是基于一个特殊的表示表面称为平方根函数（SRF）。从SRF空间拉回\（\mathbb{L}^{2}\）度量导致曲面空间上的黎曼度量。第二种方法是基于弹性表面度量。我们证明了这个度量的一个限制，我们称之为部分弹性度量，成为平方根正规场（SRNF）表示下的标准\（\mathbb{L}^{2}\）度量。我们显示了这些方法的优势，通过计算高度铰接的表面和形状统计的手动生成的表面之间的测地线路径。我们还描述了这个框架的应用程序，图像配准和医疗诊断。
We describe two Riemannian frameworks for statistical shape analysis of parameterized surfaces. These methods provide tools for registration, comparison, deformation, averaging, statistical modeling, and random sampling of surface shapes. A crucial property of both of these frameworks is that they are invariant to reparameterizations of surfaces. Thus, they result in natural shape comparisons and statistics. The first method we describe is based on a special representation of surfaces termed square-root functions (SRFs). The pullback of the \(\mathbb{L}^{2}\) metric from the SRF space results in the Riemannian metric on the space of surfaces. The second method is based on the elastic surface metric. We show that a restriction of this metric, which we call the partial elastic metric, becomes the standard \(\mathbb{L}^{2}\) metric under the square-root normal field (SRNF) representation. We show the advantages of these methods by computing geodesic paths between highly articulated surfaces and shape statistics of manually generated surfaces. We also describe applications of this framework to image registration and medical diagnosis.
影响因子：
1.3
作者：
Davatzikos, C;Vaillant, M;Bryan, RN
通讯作者：
Bryan, RN