33 citations · 116 across the 33 of their papers we have counts for
7 papers · 1 filter
Differential geometry and stochastic dynamics with deep learning numerics
Line Kühnel, Alexis Arnaudon, Stefan Sommer
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently u…
Stochastic metamorphosis with template uncertainties
Alexis Arnaudon, Darryl Holm, Stefan Sommer
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincaré theory. In the metamor…
Computational Anatomy in Theano
Line Kühnel, Stefan Sommer
To model deformation of anatomical shapes, non-linear statistics are required to take into account the non-linear structure of the data space. Computer implementations of non-linea…
Bridge Simulation and Metric Estimation on Landmark Manifolds
Stefan Sommer, Alexis Arnaudon, Line Kuhnel +1
We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition d…
A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images
Akshay Pai, Stefan Sommer, Lars Lau Raket +4
Template estimation plays a crucial role in computational anatomy since it provides reference frames for performing statistical analysis of the underlying anatomical population var…
A Geometric Framework for Stochastic Shape Analysis
Alexis Arnaudon, Darryl D. Holm, Stefan Sommer
We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is i…
Stochastic Development Regression on Non-Linear Manifolds
Line Kühnel, Stefan Sommer
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objec…