Sasaki Metric for Spline Models of Manifold-Valued Trajectories
accepted for publication
- 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 Bézier 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.
Author: | Esfandiar NavayazdaniORCiD, Felix AmbellanORCiD, Martin HanikORCiD, Christoph von TycowiczORCiD |
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Document Type: | Article |
Parent Title (English): | Computer Aided Geometric Design |
Year of first publication: | 2023 |
ArXiv Id: | http://arxiv.org/abs/arXiv:2303.17299 |