Image analysis consists of many steps which start at the acquisition of the raw data and end with a fully reconstructed, motion corrected, registered and segmented image. Each of these steps consists of many possible algorithms but in almost all cases, the analysis proceeds linearly from one step to another, without taking into account the fact that errors are propagated from step to step.

This project will look at joint modelling and analysis of such issues from both a computational analysis and statistical point of view. Variational techniques and metric based procedures can be used to align and analyse the data jointly [1,2], while incorporating such metrics into the subsequent statistical modelling is also possible [3]. A dominant difficulty in joint models is the complexity of the latter, often resulting into nonlinear and non-convex variational problems whose analysis and robust computation are challenging.  Also the well-posedness and the statistical validity of a joint analysis is non-trivial, requiring sophisticated techniques from applied analysis and statistics. The project could take on various connotations, from very theoretical considerations to computational algorithm development and investigation of different applications in image analysis.

[1] S. Ozeré, C. Le Guyader, C. Gout, Joint segmentation/registration model by shape alignment via weighted total variation minimization and nonlinear elasticity, SIAM J. on Imaging Sciences 8(3), 1981–2020, 2015.
[2] H. Dirks, Variational Methods for Joint Motion Estimation and Image Reconstruction, PhD thesis, Institute for Computational and Applied Mathematics, University of Muenster, http://wwwmath.uni-muenster.de/num/publications/2015/Dir15/.
[3] S Kurtek, H Drira. A comprehensive statistical framework for elastic shape analysis of 3D faces Computers & Graphics 51, 52–59, 2015