33 citations · 116 across the 33 of their papers we have counts for
45 papers
Principal subbundles for dimension reduction
Morten Akhøj, James Benn, Erlend Grong +2
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to o…
Long-time existence of Brownian motion on configurations of two landmarks
Karen Habermann, Philipp Harms, Stefan Sommer
We study Brownian motion on the space of distinct landmarks in , considered as a homogeneous space with a Riemannian metric inherited from a right-invariant metric on…
Sliding at first order: Higher-order momentum distributions for discontinuous image registration
Lili Bao, Jiahao Lu, Shihui Ying +1
In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration met…
A function space perspective on stochastic shape evolution
Elizabeth Baker, Thomas Besnier, Stefan Sommer
Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape m…
A Denoising Diffusion Model for Fluid Field Prediction
Gefan Yang, Stefan Sommer
We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff. By performing a diffusion process, the model is able to learn a compl…
Most probable paths for developed processes
Erlend Grong, Stefan Sommer
Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for exa…
Most probable flows for Kunita SDEs
Erlend Grong, Stefan Sommer
We identify most probable flows for Kunita Brownian motions, i.e. stochastic flows with Eulerian noise and deterministic drifts. Such stochastic processes appear for example in flu…
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…
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…
Geometry of Sample Spaces
Philipp Harms, Peter W. Michor, Xavier Pennec +1
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of the…
Diffusion bridges for stochastic Hamiltonian systems and shape evolutions
Alexis Arnaudon, Frank van der Meulen, Moritz Schauer +1
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic path…
Horizontal Flows and Manifold Stochastics in Geometric Deep Learning
Stefan Sommer, Alex Bronstein
We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a…
Simulation of Conditioned Diffusions on the Flat Torus
Mathias Højgaard Jensen, Anton Mallasto, Stefan Sommer
Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for e…
Generalizations of Ripley's K-function with Application to Space Curves
Jon Sporring, Rasmus Waagepetersen, Stefan Sommer
The intensity function and Ripley's K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many a…
Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions
Line Kühnel, Alexis Arnaudon, Tom Fletcher +1
Modelling deformation of anatomical objects observed in medical images can help describe disease progression patterns and variations in anatomy across populations. We apply a stoch…