Abstract Remco Duits

Lie Group Analysis for Medical Image Processing



Remco Duits, 

Associate Professor,

Eindhoven University of Technology.

Department of Mathematics and Computer Science,

CASA: Centre for Analysis, Scientific Computing, and Applications,

DSC/e: Data Science Center Eindhoven (Mathematical Image Analysis).

Department of Biomedical Engineering,

Imag/e (Medical Image Analysis).



R. Duits received his M.Sc. degree (cum laude) in Mathematics in 2001 at the TU/e, The Netherlands. He received his PhD-degree (cum laude) at the Department of Biomedical Engineering at the TU/e. Now 

he is associate professor at the Department of Applied Mathematics & Computer Science and affiliated part-time at the Biomedical Image Analysis group at the Biomedical Engineering Department. He has received an ERC-StG personal grant (Lie analysis, no. 335555). His research interests subtends group theory, functional analysis, differential geometry, PDE’s, harmonic analysis, geometric control and their applications to biomedical imaging and vision.



Correct automatic detection and tracking of vascular trees in MR, X-ray images and retinal images is of crucial importance for diagnosis of diseases (e.g. stenosis, artery vein malformation, diabetes), and for surgery planning. The automatic detection and tracking is very challenging and state-of-the art methods developed in industry and academia still fail in many relevant cases, due to:

1. topologically complex vascular structures involving bifurcations and crossings,

2. noisy images with low contrast (due to reduction of radiation dose or acquisition time),

3. too intensive user interaction (required for setting key-points and parameter settings).

To overcome these problems we apply automatic vessel tracking, vessel enhancement and analysis in medical images, via our Lie group techniques in orientation scores. Such an orientation score provides a comprehensive, overview of all oriented structures present in the 2D or 3D image. It enlarges the spatial image domain to the coupled space of positions and orientations, embedded in the Lie group of rigid body motions. Within the orientation score, we encode a complete disentanglement of all local orientations present in the image, allowing for generic, crossing-preserving, contextual image processing.

Applications of 2 examples of such kind of image processing will be shown:

·         Tracking and analysis of complex vascular structures in orientation scores of retinal and X-ray images. This is done along asymmetric, globally optimal, Finsler geodesics, which account for both crossings and bifurcations in vascular structures.  

·         Crossing-preserving diffusions via orientation scores of medical images. E.g. for enhancement of complex 3D vascular structures near the abdominal aorta in noisy 3D cone-beam CT scans.

In both cases we show that our approach out-performs the related method acting directly in the image domain, and promising combinations with machine learning are highlighted.

The techniques also apply to image processing of diffusion weighted MRI (DW-MRI) images, allowing for a more robust, reproducible, crossing-preserving, quantification of structural connectivity in brain-white matter. As an application (studied with Epilepsy Institute Kempenhaeghe) we consider the robust detection of the optic radiation in DW-MRI data of the brain, which is important for surgical planning in epilepsy surgery.  

The presented framework is part of a new Lie group analysis theory (solving open mathematical problems). In this talk we rather focus on its geometric intuitions, and its use for medical image processing.