16 citations · 27 across the 8 of their papers we have counts for
10 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…
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…
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…
A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks
Martha Paskin, Daniel Baum, Mason N. Dean +1
3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2…
Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms
Felix Ambellan, Stefan Zachow, Christoph von Tycowicz
We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature…
A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds
Esfandiar Nava-Yazdani, Hans-Christian Hege, Christoph von Tycowicz
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 s…
Proofs of two Theorems concerning Sparse Spacetime Constraints
Christian Schulz, Christoph von Tycowicz, Hans-Peter Seidel +1
In the SIGGRAPH 2014 paper [SvTSH14] an approach for animating deformable objects using sparse spacetime constraints is introduced. This report contains the proofs of two theorems…