Research
Generative Modeling of Appearance and Shape for Medical Image Analysis
The project focuses on classes of image data given by partitions with randomly varying geometry and fixed topology, and with class-specific appearance of each component of the partition. Variational methods will be studied for learning generative model parameters from examples and for tractable inference based on the interaction of respective model components. The application scenario concerns 3D OCT scans of the retina.
Variational Methods for Image Segmentation with Shape Priors
Prior knowledge about the shape of objects constitutes an important cue for image segmentation. Constructing shape prior functionals entails a delicate trade-off between descriptive power and mathematical and computational feasibility. Simple approaches are often unsatisfying in properly describing the set of allowed shapes, while sophisticated techniques usually yield highly non-convex functionals that are difficult to handle from the optimization point-of-view.
In this project we try to develop efficient approximations to powerful but computationally intractable shape-similarity measures and to combine them with recent progress concerning convex variational relaxations of the segmentation problem.
Inference for Highly-Connected Graphical Models
Graphical models constitute a major class for learning and object
recognition in computer vision. We focus on different types of models, including sparse large scale models and models with a high connectivity, and investigate the inference problem for this difficult case, with a wide range of potential applications, including image segmentation and object recognition. Details...
Wasserstein Distances and Variational Image Analysis
The project focuses on probabilistic representations of basic functions of variational image processing including restoration, segmentation, motion, correspondence and matching. In particular, Wasserstein distances and induced metrics and regularizers are explored in a variational framework both mathematically and computationally.
3D Industrial Object Recognition
We investigate algorithms for 3D localization and pose estimation of known components in industrial environments. The components are randomly
assembled in a large bin and partially occlude each other. Based on irregularly sampled noisy range data, we wish to solve the coupled problems of data assignment and model estimation under runtime constraints. Details...
Convex Models and Global Optimization for Image Segmentation and Labeling
In this project, we study approaches to solve combinatorial problems related to image segmentation within
the convex optimization framework. Using specially developed algorithms, these problems can be globally
optimized even for very general data terms, which allows to clearly separate modeling and optimization
eff ects. Details...
Recent Publications:
- Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem. J. Lellmann et al., EMMCVPR 2011
- Fast and Exact P-D Iterations for Variational Problems in Computer Vision. J. Lellmann et al., ECCV 2010
3D Tomography from Few Projections in Experimental Fluid Dynamics
We study the tomographic problem of reconstructing particle volume functions from few and simultaneous projections (2D images). The corresponding 3D particle image sequences provide the basis for estimating complex fluid flows directly in 3D. However the instantaneous 3D reconstructions of the tracer particles within
the fluid is an ill-posed image reconstruction problem, since the overall method employs undersamplying to make the high speed process feasible. The ill-posedness of the reconstruction problem is also aggravated by higher particle densities. On the other hand, higher densities are desirable since they increase the resolution and measurement accuracy. We investigate this trade-off phenomenon taking into account relevant developments in compressed sensing.