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.
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 analyzed from retinal fundus images.