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07/06/2023
Principal subbundles for dimension reduction
In this paper we demonstrate how sub-Riemannian geometry can be used for...
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03/14/2023
Sliding at first order: Higher-order momentum distributions for discontinuous image registration
In this paper, we propose a new approach to deformable image registratio...
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02/10/2023
A function space perspective on stochastic shape evolution
Modelling randomness in shape data, for example, the evolution of shapes...
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01/27/2023
A denoting diffusion model for fluid flow prediction
We propose a novel denoising diffusion generative model for predicting n...
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11/28/2022
Most probable paths for developed processes
Optimal paths for the classical Onsager-Machlup functional determining m...
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09/08/2022
Most probable flows for Kunita SDEs
We identify most probable flows for Kunita Brownian motions, i.e. stocha...
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08/26/2022
Tangent phylogenetic PCA
Phylogenetic PCA (p-PCA) is a version of PCA for observations that are l...
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06/17/2022
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
This paper presents the computational challenge on differential geometry...
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12/01/2021
Diffusion Mean Estimation on the Diagonal of Product Manifolds
Computing sample means on Riemannian manifolds is typically computationa...
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12/01/2021
Bridge Simulation on Lie Groups and Homogeneous Spaces with Application to Parameter Estimation
We present three simulation schemes for simulating Brownian bridges on c...
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10/29/2021
Most probable paths for anisotropic Brownian motions on manifolds
Brownian motion on manifolds with non-trivial diffusion coefficient can ...
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10/07/2021
Moment evolution equations and moment matching for stochastic image EPDiff
Models of stochastic image deformation allow study of time-continuous st...
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06/07/2021
Bridge Simulation and Metric Estimation on Lie Groups
We present a simulation scheme for simulating Brownian bridges on comple...
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05/26/2021
Simulation of Conditioned Semimartingales on Riemannian Manifolds
We present a scheme for simulating conditioned semimartingales taking va...
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05/25/2021
Diffusion Means in Geometric Spaces
We introduce a location statistic for distributions on non-linear geomet...
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03/16/2021
Prototyping Autonomous Robotic Networks on Different Layers of RAMI 4.0 with Digital Twins
In this decade, the amount of (industrial) Internet of Things devices wi...
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03/15/2021
Developing an Underwater Network of Ocean Observation Systems with Digital Twin Prototypes – A Field Report from the Baltic Sea
During the research cruise AL547 with RV ALKOR (October 20-31, 2020), a ...
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02/28/2021
Diffusion Means and Heat Kernel on Manifolds
We introduce diffusion means as location statistics on manifold data spa...
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02/10/2021
Currents and K-functions for Fiber Point Processes
Analysis of images of sets of fibers such as myelin sheaths or skeletal ...
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01/30/2021
Atlas Generative Models and Geodesic Interpolation
Generative neural networks have a well recognized ability to estimate un...
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10/15/2020
Geometry of Sample Spaces
In statistics, independent, identically distributed random samples do no...
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02/03/2020
Diffusion bridges for stochastic Hamiltonian systems with applications to shape analysis
Stochastically evolving geometric systems are studied in geometric mecha...
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09/13/2019
Horizontal Flows and Manifold Stochastics in Geometric Deep Learning
We introduce two constructions in geometric deep learning for 1) transpo...
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12/17/2018
Generalizations of Ripley's K-function with Application to Space Curves
The intensity function and Ripley's K-function have been used extensivel...
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12/13/2018
Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions
Modelling deformation of anatomical objects observed in medical images c...
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11/09/2018
An Average of the Human Ear Canal: Recovering Acoustical Properties via Shape Analysis
Humans are highly dependent on the ability to process audio in order to ...
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10/03/2018
PADDIT: Probabilistic Augmentation of Data using Diffeomorphic Image Transformation
For proper generalization performance of convolutional neural networks (...
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05/19/2018
Latent Space Non-Linear Statistics
Given data, deep generative models, such as variational autoencoders (VA...
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05/15/2018
String Methods for Stochastic Image and Shape Matching
Matching of images and analysis of shape differences is traditionally pu...
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01/31/2018
An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data
We provide a probabilistic and infinitesimal view of how the principal c...
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12/22/2017
Differential geometry and stochastic dynamics with deep learning numerics
In this paper, we demonstrate how deterministic and stochastic dynamics ...
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11/20/2017
Stochastic metamorphosis with template uncertainties
In this paper, we investigate two stochastic perturbations of the metamo...
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06/15/2017
Computational Anatomy in Theano
To model deformation of anatomical shapes, non-linear statistics are req...
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05/31/2017
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estima...
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03/29/2017
A Geometric Framework for Stochastic Shape Analysis
We introduce a stochastic model of diffeomorphisms, whose action on a va...
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03/01/2017
Stochastic Development Regression on Non-Linear Manifolds
We introduce a regression model for data on non-linear manifolds. The mo...
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12/16/2016
A Stochastic Large Deformation Model for Computational Anatomy
In the study of shapes of human organs using computational anatomy, vari...
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04/18/2016
Most Likely Separation of Intensity and Warping Effects in Image Registration
This paper introduces a class of mixed-effects models for joint modeling...
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12/23/2014
Symmetry in Image Registration and Deformation Modeling
We survey the role of symmetry in diffeomorphic registration of landmark...
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12/23/2014
Higher-order Spatial Accuracy in Diffeomorphic Image Registration
We discretize a cost functional for image registration problems by deriv...
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12/14/2011