Sasaki Metric for Spline Models of Manifold-Valued Trajectories
This work addresses the challenge of modeling and comparing trajectories on manifolds, such as hurricane tracks, with incremental improvements in computational efficiency and classification accuracy.
The authors tackled the problem of analyzing manifold-valued trajectories by proposing a spatiotemporal framework using composite Bézier splines and the Sasaki metric, resulting in superior performance for hurricane track intensity classification compared to state-of-the-art methods.
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.