3 citations · 8 across the 8 of their papers we have counts for
9 papers
Stochastic Completeness for Landmark Shape Spaces with Induced Metrics
Karen Habermann, Mao Nishino, Stefan Sommer
Landmark shape spaces arise from configurations of distinct landmarks with rigid motions factored out and scale normalized. When equipped with sufficiently regular metrics inhe…
Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
Gary P. T. Choi, Khanh Dao Duc, Shira Faigenbaum-Golovin +6
A central objective of machine learning is to identify structure and patterns in data. Advances in data acquisition have increasingly produced datasets whose observations possess r…
Stochastic completeness for landmark space
Karen Habermann, Stefan Sommer
We study stochastic completeness for landmark spaces equipped with Riemannian metrics induced by right-invariant metrics on subgroups of the diffeomorphism group of the shape domai…
Brownian motion on spaces of discrete regular curves
Karen Habermann, Emmanuel Hartman
We introduce and study Brownian motion on spaces of discrete regular curves in Euclidean space equipped with discrete Sobolev-type metrics. It has been established that these space…
Characterization of geodesic completeness for landmark space
Karen Habermann, Stephen C. Preston, Stefan Sommer
We provide a full characterization of geodesic completeness for spaces of configurations of landmarks with smooth Riemannian metrics that satisfy a rotational and translation invar…
Score matching for sub-Riemannian bridge sampling
Erlend Grong, Karen Habermann, Stefan Sommer
Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst si…
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…
Asymptotic error in the eigenfunction expansion for the Green's function of a Sturm-Liouville problem
Karen Habermann
We study the asymptotic error arising when approximating the Green's function of a Sturm-Liouville problem through a truncation of its eigenfunction expansion, both for the Green's…
Cartan connections for stochastic developments on sub-Riemannian manifolds
Ivan Beschastnyi, Karen Habermann, Alexandr Medvedev
Analogous to the characterisation of Brownian motion on a Riemannian manifold as the development of Brownian motion on a Euclidean space, we construct sub-Riemannian diffusions on…