Guest talk: Dr. Erik Bekkers (11.01.2018)

On January 11th, 2018, Dr. Erik Bekkers, Technische Universiteit Eindhoven, is visiting the research training group (invited by Emily King). We cordially invite you to his talk titled:

Medical Image Analysis using Sub-Riemannian Geometry in SE(2)
Thursday 11th January 2018, 14:00, room MZH 4140, MZH building, Bibliothekstr. 5.


Abstract
Medical Image Analysis using Sub-Riemannian Geometry in SE(2)
This presentation focusses on the application of sub-Riemannian geometry in 2D medical image analysis. In the analysis, 2D retinal images are lifted to 3D functions on the coupled space of positions and orientations. Lifting is done via a wavelet-type (invertible) transformation, leading to a neat organization of image data based on position and orientation. In the extended domain, which we identify with the Lie group SE(2), a sub-Riemannian (SR) geometry is recognized. Here, “sub” refers to the restriction that tangent vectors of naturally lifted curves are contained in a sub-space of the full tangent space. A parallel can be drawn between these curves and the paths of moving cars: a car can only move forward and change direction (2 controls) in a 3D state-space (2D position and orientation), but is not able to move sideways.
In this presentation the following items are discussed:
- A brief introduction to the Lie group SE(2).
- An explanation of the sub-Riemannian geometry.
- An explanation of the construction of functions on SE(2) via a wavelet-type transform (invertible orientation score transform).
- Several methods and algorithms based on the above theory with application to vessel tracking (sub-Riemannian geodesics), local curvature estimation (exponential curve fits in SE(2)), object recognition (machine learning via densities on SE(2)).
- A highlighting of some recent extensions to 3D image processing via the Lie group SE(3)