17 citations · 42 across the 12 of their papers we have counts for
15 papers
Bi-invariant Geodesic Regression: Existence, Uniqueness, and Convergence
Martin Hanik, Christoph von Tycowicz
Bi-invariant geodesic regression generalizes linear regression to Lie groups. Its main feature is that it respects the symmetries of the group so that the resulting estimator is in…
p-Laplacians for Manifold-valued Hypergraphs
Jo Andersson Stokke, Ronny Bergmann, Martin Hanik +1
Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we d…
Bi-invariant Geodesic Regression with Data from the Osteoarthritis Initiative
Johannes Schade, Christoph von Tycowicz, Martin Hanik
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in…
Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups
Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz
Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their di…
De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application
Martin Hanik, Esfandiar Nava-Yazdani, Christoph von Tycowicz
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 scienti…
Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs
Martin Hanik, Gabriele Steidl, Christoph von Tycowicz
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion l…
Intrinsic shape analysis in archaeology: A case study on ancient sundials
Martin Hanik, Benjamin Ducke, Hans-Christian Hege +2
This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all the shape informatio…
Sasaki Metric for Spline Models of Manifold-Valued Trajectories
Esfandiar Nava-Yazdani, Felix Ambellan, Martin Hanik +1
We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical…
Predicting Shape Development: a Riemannian Method
Doğa Türkseven, Islem Rekik, Christoph von Tycowicz +1
Predicting the future development of an anatomical shape from a single baseline observation is a challenging task. But it can be essential for clinical decision-making. Research ha…
SHREC 2022 Track on Online Detection of Heterogeneous Gestures
Ariel Caputo, Marco Emporio, Andrea Giachetti +10
This paper presents the outcomes of a contest organized to evaluate methods for the online recognition of heterogeneous gestures from sequences of 3D hand poses. The task is the de…
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
Adele Myers, Saiteja Utpala, Shubham Talbar +25
This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learn…
A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds
Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential…
Predicting cognitive scores with graph neural networks through sample selection learning
Martin Hanik, Mehmet Arif Demirtaş, Mohammed Amine Gharsallaoui +1
Analyzing the relation between intelligence and neural activity is of the utmost importance in understanding the working principles of the human brain in health and disease. In exi…
Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis
Martin Hanik, Hans-Christian Hege, Christoph von Tycowicz
We propose generalizations of the Hotelling's statistic and the Bhattacharayya distance for data taking values in Lie groups. A key feature of the derived measures is that th…
Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines
Martin Hanik, Hans-Christian Hege, Anaja Hennemuth +1
Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been…