Mathematical Image Analysis (MIA)

Main research interest

Development of new methodologies and algorithms for the representation and analysis of complex imaging data (`big images’) for healthcare applications. We are interested in  inverse problems, such as

  • inference of brain anatomy from diffusion weighted magnetic resonance imaging (tractography, connectivity)
  • extraction and analysis of vascular trees from retinal fundus imaging
  • detection, enhancement, completion, and geometric analysis of elongated structures in 2- and 3-dimensional images
  • myocardial motion, deformation and strain analysis from tagging magnetic resonance imaging

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
  • the theory of ordinary and partial differential equations

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
  • isotropic and anisotropic resolution of images can be  ameliorated for global deblurring or enhancement of elongated structures
  • retinal vascular trees can be robustly extracted and analysed from retinal fundus images

Project examples

  1. Lie Group Analysis for Medical Image Processing ERC StG, Remco Duits
  2. Riemann-Finsler Geometry for Human Brain Connectomics NWO, Luc Florack & Andrea Fuster
  3. Differential Geometry in Complex Medical Imaging & Relativity Theory FOM, Andrea Fuster