Jan Lellmann - Research

Drag to perform a rigid registration
(implementation by L. König)
We focus on modelling application-specific prior knowledge in image processing. Precisely formulating such prior knowledge in the form of an energy function makes it possible to systematically develop image processing methods that are more accurate and require less data. The resulting problems are often non-differentiable and high- or infinite-dimensional, which requires the development of new numerical optimization methods. we focus in particular on problems with combinatorial aspects, where a number of discrete decisions has to be made, such as the image segmentation problem.Application areas include processing and analysis of images, videos, as well as general two- and higher-dimensional data, such as directional, tensor-, or height data in medicine, biology, and earth sciences.

Keywords

  • Variational and energy minimization methods in data processing
  • Regularization strategies and modelling prior knowledge
  • Convex relaxation methods for combinatorial problems
  • Sparsity and adaptive regularization
  • Large-scale non-smooth optimization
  • Optimal transport
  • Processing of non-scalar data - directions, tensors, manifolds

Applications and Projects

  • Image restoration - denoising, deblurring, inpainting
  • Image segmentation
  • Earth sciences - Reconstruction and interpolation of digital elevation maps, analysis of LiDAR- and hyperspectral data
  • Medical image analysis - Segmentation and analysis of MRI data of thalamic nuclei

Collaborators

  • Björn Andres
  • Daniel Cremers
  • Emanuel Laude
  • Frank Lenzen
  • Dirk Lorenz
  • Thomas Möllenhoff
  • Michael Möller
  • Jean-Michel Morel
  • Kostas Papafitsoros
  • Christoph Schnörr
  • Carola-Bibiane Schönlieb
  • Daniel Spector
  • Xue-Cheng Tai
  • Tuomo Valkonen