Applied Geometry

October 2021: We have open phd and postdoc positions on stochastic processes and shape analysis with applications in biology. Please see this link or contact Stefan Sommer.

Large classes of observed data exhibit complex nonlinear structure. For example, human organs vary nonlinearly in shape, spherical images cannot be analyzed with classical convolutional neural networks due to the curvature of the spherical domain, and particles in a fluid flow interact nonlinearly. Nonlinearity makes geometry a central discipline for modeling dynamics, performing statistical analysis of complex data, and applying machine learning methods to learn from observed nonlinear data.

Riemannian Geometric Statistics in Medical Image Analysis cover

The research activities in the Applied Geometry group focus on using theory and techniques from the mathematical field of differential geometry to advance data analysis methodology. This happens at a foundational level where fundamental aspects of statistics of nonlinear data are investigated, in applied uses of geometry in e.g. shape analysis of medical data, and on the machine learning side when defining models for neural networks that handles geometric data.

The book Riemannian Geometric Statistics in Medical Image Analysis (Elsevier, 2019) describes many of the complexities and challenges of working with geometric data with a focus on medical applications.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

People

Name Title Phone E-mail
Mathias Højgaard Jensen PhD Fellow +4560609254 E-mail
Stefan Horst Sommer Professor +4535335716 E-mail