Research Output per year

# 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

## Fingerprint Dive into the research topics where Mathematical Image Analysis is active. These topic labels come from the works of this organisation's members. Together they form a unique fingerprint.

##
Network
Recent external collaboration on country level. Dive into details by clicking on the dots.

## Profiles

## Erik J. Bekkers

- Department of Mathematics and Computer Science, Mathematical Image Analysis
- Department of Mathematics and Computer Science, Centre for Analysis, Scientific Computing, and Applications W&I - Assistant Professor

Person: UD : Assistant Professor, PD : Postdoc

## Remco Duits

- Department of Mathematics and Computer Science, Centre for Analysis, Scientific Computing, and Applications W&I - Associate Professor
- Department of Mathematics and Computer Science, Mathematical Image Analysis

Person: UHD : Associate Professor

## Luc M.J. Florack

- Department of Mathematics and Computer Science, Centre for Analysis, Scientific Computing, and Applications W&I - Full Professor
- Department of Mathematics and Computer Science, Centre for Analysis, Scientific Computing, and Applications - Full Professor
- Department of Mathematics and Computer Science, Mathematical Image Analysis

Person: HGL : Professor

## Research Output

## On the non metrizability of Berwald Finsler spacetimes

Fuster, A., Heefer, S., Pfeifer, C. & Voicu, N., 1 May 2020, In : Universe. 6, 5, 12 p., 64.Research output: Contribution to journal › Article › Academic › peer-review

## Automated tractography of four white matter fascicles in support of brain tumor surgery

Meesters, S., Rutten, G-J., Fuster, A. & Florack, L., 2019,*Proceedings of the Organization for Human Brain Mapping annual meeting.*1 p.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

## Fourier transform on the homogeneous space of 3D positions and orientations for exact solutions to linear PDEs

Duits, R., Bekkers, E. J. & Mashtakov, A., 8 Jan 2019, In : Entropy. 21, 1, 38 p., 38.Research output: Contribution to journal › Article › Academic › peer-review

## Prizes

## Context-aware Artificial Intelligence in medical image analysis

Erik Bekkers (Recipient), Jul 2019

Prize: NWO › Veni › Scientific

## MICCAI Young Scientist Award

Erik J. Bekkers (Recipient), 19 Sep 2018

Prize: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Philips Impact Award

Erik J. Bekkers (Recipient), 6 Jun 2018

Prize: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Activities

- 1 Keynote talk

## Riemannian and Finslerian Geometry for Diffusion Weighted Magnetic Resonance Imaging

Luc Florack (Speaker)Activity: Talk or presentation types › Keynote talk › Scientific

## Press / Media

## The Mathematics Round Table: an introduction

22/08/19

1 item of Media coverage

Press/Media: Expert Comment

## Eindhoven University of Technology: Five Veni Grants - From Energy Storage to Artificial Neurons

Erik J. Bekkers, Weiming Yao, S.C. (Lenneke) Kuijer & Antoni Forner Cuenca

16/07/19

1 item of Media coverage

Press/Media: Expert Comment

## Student theses

## 3D reconstruction of streamer discharges using mathematical algorithms: based on predictive back-end reconstruction, minimum spanning trees and sub-Riemannian geometry

Author: de Veld, F., 4 Jul 2019Supervisor: Dijcks, S. (Supervisor 1), Nijdam, S. (Supervisor 2), Bekkers, E. (Supervisor 2) & Florack, L. (Supervisor 2)

Student thesis: Bachelor

## Geometric image denoising and machine learning

Author: Smets, B., 2019Supervisor: Duits, R. (Supervisor 1), Bekkers, E. (Supervisor 2) & Portegies, J. W. (Supervisor 2)

Student thesis: Master