Vaillant M, Miller M I, Younes L, Trouvé A
Center for Imaging Science, The Johns Hopkins University, Baltimore, MD 21218, USA.
Neuroimage. 2004;23 Suppl 1:S161-9. doi: 10.1016/j.neuroimage.2004.07.023.
In this paper, we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point along the geodesic is completely determined by the momentum at the origin through geodesic shooting equations. The space of initial momentum provides a linear representation of the nonlinear diffeomorphic shape space in which linear statistical analysis can be applied. Specializing to the landmark matching problem of Computational Anatomy, we derive an algorithm for solving the variational problem with respect to the initial momentum and demonstrate principal component analysis (PCA) in this setting with three-dimensional face and hippocampus databases.
在本文中，我们提出了一种用于形状统计分析的线性框架以及一种基于最近推导的微分同胚流测地线动量守恒定律的优化方法。一旦模板固定，初始动量空间就成为通过测地线流研究形状的合适空间，因为沿着测地线任何一点的流完全由原点处的动量通过测地线发射方程确定。初始动量空间提供了非线性微分同胚形状空间的线性表示，在其中可以应用线性统计分析。专门针对计算解剖学的地标匹配问题，我们推导了一种关于初始动量求解变分问题的算法，并在三维面部和海马体数据库的这种情况下展示了主成分分析（PCA）。
