Computing Diffeomorphic Paths for Large Motion Interpolation.
Computing Diffeomorphic Paths for Large Motion Interpolation.
复制标题
DOI：
10.1109/cvpr.2013.162
复制
发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Vemuri BC
中科院分区：
文献类型：
--
作者：
Seo D;Jeffrey H;Vemuri BC
在本文中，我们介绍了一种新的框架计算之间的一对输入的同构的同构路径。直接计算Diff（Ω）空间上的测地线是困难的，这主要归因于Diff（Ω）的无穷维性。我们提出的框架在一定程度上绕过了这个困难，使用Diff（Ω）到商空间Diff（M）/Diff（M）μ的商映射，该商空间是通过排除保体积同态Diff（M）μ的子群而获得的。这个商空间最近在数学文献中被确定为Hilbert空间中的单位球，Hilbert空间是一个具有众所周知的几何性质的空间。我们的框架利用这一最新的结果，通过计算两个阶段的同构路径。首先，我们将给定的仿射对投影到这个球面上，然后计算这些投影点之间的测地线路径。其次，我们解除球面上的测地线回空间的拓扑异构，通过解决一个二次规划问题的双线性约束，使用增广拉格朗日技术与惩罚条款。通过这种方式，我们可以估计的路径，第一，停留在空间中的变形同态，第二，保持形状/体积的变形图像沿着路径尽可能多。我们已经应用我们的框架内插帧子采样视频序列的中间帧。在报告的实验中，我们的方法相比，毫不逊色流行的大变形几何度量映射框架（LDDMM）。
In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff(Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff(Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map of Diff(Ω) to the quotient space Diff(M)/Diff(M)μ obtained by quotienting out the subgroup of volume-preserving diffeomorphisms Diff(M)μ. This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).