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Sasaki Metric for Spline Models of Manifold-Valued Trajectories

  • 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
Document Type:Article
Parent Title (English):Computer Aided Geometric Design
Year of first publication:2023
ArXiv Id:http://arxiv.org/abs/arXiv:2303.17299
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