Mathematical Image Analysis

  • Address

    Groene Loper 5, Metaforum

    5612 AP Eindhoven

    Netherlands

Organization profile

Introduction / mission

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

Highlighted phrase

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

Organisational profile

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

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. Our work contributes towards the following SDG(s):

  • SDG 3 - Good Health and Well-being

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  • Anisotropy Across Fields and Scales

    Özarslan, E. (ed.), Schultz, T. (ed.), Zhang, E. (ed.) & Fuster, A. (ed.), 2021, Springer. (Mathematics and Visualization; vol. 4562)

    Research output: Book/ReportBook editingAcademicpeer-review

    Open Access
  • A Novel Algorithm for Region-to-Region Tractography in Diffusion Tensor Imaging

    Smolders, L., Sengers, R., Fuster, A., de Berg, M. & Florack, L., 2021, Computational Diffusion MRI : 12th International Workshop, CDMRI 2021, Held in Conjunction with MICCAI 2021, Strasbourg, France, October 1, 2021, Proceedings. Cetin-Karayumak, S., Christiaens, D., Figini, M., Guevara, P., Gyori, N., Nath, V. & Pieciak, T. (eds.). Cham: Springer, p. 71-81 11 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 13006 )(Image Processing, Computer Vision, Pattern Recognition, and Graphics (LNIP); vol. 13006).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

  • Automatic tractography for brain tumor surgery: towards clinical application

    Meesters, S., Landers, M., Rutten, G-J. & Florack, L., 2021, Proceedings of the ISMRM & SMRT Annual Meeting & Exhibition 15-20 May 2021.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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