In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.

翻译：在许多应用中,大地测量等级模型足以用于研究时间观测,我们采用这种模型,为肯德尔的形状空间提供多重价值数据,特别是,我们采用这种模型,而不是佐木测量,而采用基于功能的测量方法,提高计算效率,不要求实施曲线温度,我们建议相应的大地测量变化时间分化,并采用2D大鼠头骨形状和3D形状的纵向分析方法,这些形状来自对骨髓炎的成像研究,我们进行假设测试,估计平均趋势。