33 citations · 116 across the 33 of their papers we have counts for
10 papers · 1 filter
Diffusion Mean Estimation on the Diagonal of Product Manifolds
Mathias Højgaard Jensen, Stefan Sommer
Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fréchet mean which often requires finding minimizing geodesi…
Bridge Simulation and Metric Estimation on Lie Groups and Homogeneous Spaces
Mathias Højgaard Jensen, Lennard Hilgendorf, Sarang Joshi +1
We present schemes for simulating Brownian bridges on complete and connected Lie groups and homogeneous spaces. We use this to construct an estimation scheme for recovering an unkn…
Most probable paths for anisotropic Brownian motions on manifolds
Erlend Grong, Stefan Sommer
Brownian motion on manifolds with non-trivial diffusion coefficient can be constructed by stochastic development of Euclidean Brownian motions using the fiber bundle of linear fram…
Moment evolution equations and moment matching for stochastic image EPDiff
Alexander Christgau, Alexis Arnaudon, Stefan Sommer
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medica…
Bridge Simulation and Metric Estimation on Lie Groups
Mathias Højgaard Jensen, Sarang Joshi, Stefan Sommer
We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian…
Simulation of Conditioned Semimartingales on Riemannian Manifolds
Mathias Højgaard Jensen, Stefan Sommer
We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean br…
Diffusion Means in Geometric Spaces
Benjamin Eltzner, Pernille Hansen, Stephan F. Huckemann +1
We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fréchet mean. The diffusio…
Diffusion Means and Heat Kernel on Manifolds
Pernille Hansen, Benjamin Eltzner, Stefan Sommer
We introduce diffusion means as location statistics on manifold data spaces. A diffusion mean is defined as the starting point of an isotropic diffusion with a given diffusivity. T…
Currents and K-functions for Fiber Point Processes
Pernille EH. Hansen, Rasmus Waagepetersen, Anne Marie Svane +4
Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necess…
Atlas Generative Models and Geodesic Interpolation
Jakob Stolberg-Larsen, Stefan Sommer
Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not p…