We are looking for a Post-doctoral researcher at the Department of Mathematics & Computer Science of the Eindhoven University of Technology in the field of 'Geometric Learning for Image Analysis'.
This post-doc position is part of VICI Project (VI.C. 2020-031, PI: R.Duits) and requires knowledge of geometric image processing and deep learning.
Applied Differential Geometry cluster at the Mathematics department collaborating in the Eindhoven Artificial Intelligence Systems Institute (EAISI).
Below we first provide a description of the overall VICI project 'Geometric Learning for Image Analysis', and then we address the specific tasks of this post-doctoral research position.Overall Research Project description
We develop a new geometric deep learning framework for convolutional neural networks (CNNs) with a firm mathematical foundation, relying on partial differential equations (PDEs), differential geometry, Lie group analysis, and probability theory. It impacts mathematics by providing new fundamental theorems on higher dimensional homogeneous spaces. It also impacts medical image analysis, solving major challenges in tracking and enhancement of complex vasculature.
Current geometric algorithms allow for geometric understanding of image analysis, but often fail at complex line structures (crossings, bifurcations), requiring costly user-interaction. Deep learning algorithms via CNNs perform superbly on specific datasets, but require massive annotations for training, lack geometric model interpretability, and fail to hard-code necessary equivariances.
We aim to bridge geometrical data-processing and machine learning based data-processing. To cope with complex structures in tracking and enhancement we lift image data to higher dimensional homogeneous spaces. To reduce manual input we use geometric PDE-based data processing and training. To reduce highly redundant annotations we develop new equivariant CNNs arising from operator splitting of geometric PDEs.
To underpin our algorithms we will establish new theories and mathematical foundations for geometric learning and control on homogeneous spaces. We validate our algorithms in automatic enhancement and tracking of complex line structures in medical images, where reduction of user-input is crucial.
We tackle this by applying our geometric learning algorithms on (multi-orientation) image-representations on homogeneous spaces.
This novel geometrical learning framework will generalize fundamental results on analysis, geometry, and probability theory to homogeneous spaces, and produce a new generation of geometric PDE-based CNNs and powerful image analysis algorithms that overcome costly user-interactions and annotations.NB. An extensive project description is available on request. Task Description of the Post-doctoral Researcher within the Project.
1. Carry out research within the team (2 PhDs, 1 PhD-TA, 1 post-doc, 1 scientific programmer) supervised by principal investigator Remco Duits,www.tue.nl/en/news/news-overview/14-04-2021-vici-grant-for-mathematician-remco-duits/
, focusing on:
- Automatic geometric vessel tree tracking and analysis, and crossing-preserving connectivity measures, in medical image analysis applications (optical images, X-ray),
- Equivariant, PDE-based Processing and Machine Learning for Image Analysis (segmentation of vascular trees and diagnosis of diseases),
2. Assist in the supervision of PhD students and collaborate with health tech partners,
3. Report on the results in project deliverables, papers and conference contributions.
Finally, a small contribution to the teaching activities of the Applied Differential Geometry cluster in the mathematics department may be asked.