@article{NavayazdaniAmbellanHaniketal., author = {Navayazdani, Esfandiar and Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Sasaki Metric for Spline Models of Manifold-Valued Trajectories}, series = {Computer Aided Geometric Design}, volume = {104}, journal = {Computer Aided Geometric Design}, doi = {10.1016/j.cagd.2023.102220}, pages = {102220}, abstract = {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{\´e}zier 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.}, language = {en} } @inproceedings{Navayazdani, author = {Navayazdani, Esfandiar}, title = {Elastic Analysis of Augmented Curves and Constrained Surfaces}, series = {Proc. of IAPR Third International Conference on Discrete Geometry and Mathematical Morphology}, booktitle = {Proc. of IAPR Third International Conference on Discrete Geometry and Mathematical Morphology}, publisher = {Springer}, doi = {https://link.springer.com/chapter/10.1007/978-3-031-57793-2_27}, pages = {353 -- 363}, language = {en} }