@article{NavaYazdaniHegevonTycowicz, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds}, series = {Journal of Mathematical Imaging and Vision}, volume = {64}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-022-01079-x}, pages = {395 -- 407}, abstract = {In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.}, language = {en} } @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} } @article{HanikNavayazdanivonTycowicz, author = {Hanik, Martin and Navayazdani, Esfandiar and von Tycowicz, Christoph}, title = {De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application}, series = {Computer Aided Geometric Design}, volume = {110}, journal = {Computer Aided Geometric Design}, doi = {10.1016/j.cagd.2024.102288}, pages = {102288}, abstract = {For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.}, language = {en} } @article{Navayazdani, author = {Navayazdani, Esfandiar}, title = {On Geodesics in the Spaces of Constrained Curves}, series = {Journal of Differential Geometry and its Applications}, journal = {Journal of Differential Geometry and its Applications}, abstract = {In this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of some results on planar concentric circles to surfaces. The work focuses on intrinsic and constructive approaches.}, 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} } @article{VeldhuijzenVeltkampIkneetal., author = {Veldhuijzen, Ben and Veltkamp, Remco C. and Ikne, Omar and Allaert, Benjamin and Wannous, Hazem and Emporio, Marco and Giachetti, Andrea and LaViola Jr, Joseph J. and He, Ruiwen and Benhabiles, Halim and Cabani, Adnane and Fleury, Anthony and Hammoudi, Karim and Gavalas, Konstantinos and Vlachos, Christoforos and Papanikolaou, Athanasios and Romanelis, Ioannis and Fotis, Vlassis and Arvanitis, Gerasimos and Moustakas, Konstantinos and Hanik, Martin and Nava-Yazdani, Esfandiar and von Tycowicz, Christoph}, title = {SHREC 2024: Recognition Of Dynamic Hand Motions Molding Clay}, series = {Computers \& Graphics}, volume = {123}, journal = {Computers \& Graphics}, doi = {10.1016/j.cag.2024.104012}, pages = {104012}, abstract = {Gesture recognition is a tool to enable novel interactions with different techniques and applications, like Mixed Reality and Virtual Reality environments. With all the recent advancements in gesture recognition from skeletal data, it is still unclear how well state-of- the-art techniques perform in a scenario using precise motions with two hands. This paper presents the results of the SHREC 2024 contest organized to evaluate methods for their recognition of highly similar hand motions using the skeletal spatial coordinate data of both hands. The task is the recognition of 7 motion classes given their spatial coordinates in a frame-by-frame motion. The skeletal data has been captured using a Vicon system and pre-processed into a coordinate system using Blender and Vicon Shogun Post. We created a small, novel dataset with a high variety of durations in frames. This paper shows the results of the contest, showing the techniques created by the 5 research groups on this challenging task and comparing them to our baseline method.}, language = {en} }