We are interested in inverse problems, such as: 

• Inference of brain anatomy from diffusion weighted magnetic resonance imaging (tractography, connectivity)
• Detection, enhancement, completion, and geometric analysis of elongated structures in 2-and 3-dimensional images
• AI enhanced geometric image analysis

Development of new methodologies and algorithms for the representation and analysis of complex imaging data (`big images’) for healthcare applications.

Our methodological approach relies on a broad spectrum of mathematical techniques, such as
• Finsler geometry
• tensor calculus
• Lie group theory
• calculus of variations
• geometric control theory
• semigroup theory for multiresolution
representations
• ordinary and partial differential equations
• deep learning

We are also interested in methodological tangencies with other scientific disciplines, such as theoretical physics, e.g.
• mathematical relativity

Success stories
The group has conducted several feasibility studies establishing proof of concept for clinical applications, such as
• myocardial motion, deformation, and strain can be obtained for myocardial function analysis from tagging magnetic resonance imaging
• the optic radiation can be delineated including the Meyer’s tip for temporal lobe resection therapy planning and risk analysis from diffusion weighted magnetic resonance imaging
• retinal vascular trees can be robustly extracted and analyzed from retinal fundus images

Project examples
1. Lie Group Theory & Differential Geometry for Medical Image Analysis, Remco Duits
2. Riemann-Finsler Geometry for Brain Connectivity and Tractography, Luc Florack & Andrea Fuster
3. Differential Geometry in Complex Medical Imaging & Relativity Theory, Andrea Fuster
4. Roto-Translation Covariant Convolutional Networks for Medical Image Analysis, Erik Bekkers