We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite B\' ezier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks.

翻译：我们提出了一个通用的时空框架来分析流形值测量，它允许使用一种内在的和计算效率高的Riemannian分层模型。特别地，利用回归，我们将离散轨迹在Riemannian流形中表示为复合Bézier样条，提出了一种由Sasaki度量诱导的自然度量来比较轨迹，并估计平均轨迹作为群体趋势。我们在飓风轨迹的定性和定量实验中将我们的框架与最先进的方法进行比较。值得注意的是，我们的结果证明了样条基础方法在轨迹强度分类方面的优越性。