Image of Me

Aasa Feragen, Post-doc

Direct: (+45) 353 20739
Email : aasa@diku.dk
Office: HCØ - Building E, Office 4.0.4
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A Short Description

Hi, my name is Aasa, and I am a mathematician.

My research focuses on the analysis of data which naturally lives in non-smooth spaces, and tree-structured data in particular. One example of tree-structured data is the human airway tree. CT scanning is providing us with large amounts of information about the geometry of airway trees, but we lack the statistical methods to analyze these types of data. Which is lucky for me, since this gives rise to interesting problems at the intersection of geometry, statistics, algorithms, anatomical modeling and medical image analysis.

Airway trees are examples of anatomical tree-structured data.

Ancient history

I received my PhD in pure mathematics from the university of Helsinki in February 2010, with the thesis "Topological stability through tame retractions". My PhD research centered around singularity theory, symmetry in the form of Lie group actions, and the overlap of these research areas. I spent the academic years 2006-2009 as a visiting student at Aarhus University, where I worked under the supervision of Andrew du Plessis.

Since September 2009 I have been working as a post doc in the Image group at the eScience Center at DIKU, University of Copenhagen, where I work with Francois Lauze and Mads Nielsen. Since January 2010 I have been funded by a postdoctoral project grant from the Lundbeck foundation.

Research

The topic of my current research is mathematical image analysis, in particular statistical methods for tree-structured data. The aim of my project is to develop methods for doing statistical analysis such as finding an average or analyzing variation in a dataset where the objects have the structure of a tree (or, more generally, a graph) with deformable features associated to the edges. Whereas the main goal of the project is to develop theoretical foundations, we find motivation and applications in medical imaging, where we use our methods to do pattern recognition based on the shape of airway trees.

Before joining the image group, my research had two focus areas: topological aspects of singularities of smooth maps, and symmetry through the action of Lie groups. Some of my work on Lie group actions takes place in the setting of general metric spaces; however, Lie group actions also enter my research in singularity theory through my work on groups of (multi)germ equivalences, which are key tools for understanding and solving local-to-global problems for singularities of smooth maps. The main topic of my PhD thesis was sufficient conditions for topological stability through the so-called extremely tame retractions, whose fibers form non-smooth foliations. This placed me in the intersection of differential topology, real algebraic geometry and Lie group actions.

My CV: short version, long version.

Publications and theses

Journals

A. Feragen, P. Lo, M. de Bruijne, M. Nielsen, F. Lauze: Towards a theory of statistical tree-shape analysis, submitted 2011.
A. A. du Plessis, A. Feragen: Topology of groups of multigerm equivalences (preliminary version), 2009.
A. A. du Plessis, A. Feragen: Topological stability through extremely tame retractions to appear in Topology and its Applications, 2009.
A. Feragen: Equivariant embedding of metrizable G-spaces in linear G-spaces, Proc. Amer. Math. Soc. 136 (2008), 2985-2995.

Conferences

A. Feragen, P. Lo, V. Gorbunova, M. Nielsen, A. Dirksen, J. Reinhardt, F. Lauze, M. de Bruijne: An airway tree-shape model for geodesic airway branch labeling, Mathematical Foundations for Computational Anatomy Workshop, MICCAI 2011.
A. Feragen, S. Hauberg, M. Nielsen, F. Lauze: Means in spaces of treelike shapes, accepted at the International Conference of Computer Vision (ICCV) 2011.
A. Feragen, F. Lauze, P. Lo, M. de Bruijne, M. Nielsen: Geometries on spaces of treelike shapes, ACCV, 2010.
A. Feragen, F. Lauze, M. Nielsen: Fundamental geodesic deformations in spaces of treelike shapes, ICPR, 2010.
A. Feragen: An equivariant Tietze extension theorem for proper actions of locally compact groups, EWM Proceedings of the 13th General Meeting University of Cambridge, UK, 3 -- 6 September 2007. red. Sylvie Paycha ; Catherine Hobbs. 2010.

Theses

A. Feragen: Topological stability through tame retractions, Annales Academiae Scientiarum Fennicae Mathematica Dissertationes 154, 2009, (PhD thesis).
A. Feragen: Characterization of equivariant ANEs, Licentiate thesis, 2006.
A. Feragen: A topological manifold is homotopy equivalent to some CW complex, Master's thesis, 2004.

Other work

A. Feragen, M. Nielsen, S. Hauberg, P. Lo, M. de Bruijne and F. Lauze: A geometric framework for statistics on trees, Technical report, April 2011.
A. Feragen: A short and elementary proof of Hanner's theorem, preprint.

Extracurricular research

In addition to my work on mathematics, some of my time in Copenhagen has been spent on the much-too-ignored basic research topic of Limfjordsporter cake. You haven't had chocolate cake until you have had this one.

Check out the technical report!

Projects, Collaborations, and Software

Supplementary material: Means in spaces of treelike shapes (ICCV 2011)

Supplementary material: Fundamental geodesic deformations in spaces of treelike shapes (ICPR 2010)

Supplementary material: Geometries on spaces of treelike shapes (ACCV, 2010)

Links

Summer school on Sparsity in Image and Signal Analysis
Singularities in Aarhus, August 17-21, 2009
The 3rd Nordic EWM summer school for PhD students in Mathematics, June 22-27, 2009
The Department of Mathematics and Statistics at the University of Helsinki
The Department of Mathematical Sciences at Aarhus University
The European Women in Mathematics