The RTG has started in April 2010.
- Variational Methods For Graphical Models with Discrete Random Variables
Many tasks of computational image analysis routinely involve contextual discrete decisions. The project focuses on models defined on graphs with low connectivity and corresponding polyhedral relaxations of the inference problem. The research work will focus on variational methods and problem decompositions that enable inference and learning using more expressive models.
- 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.
- Multivariate Predictive Distributions of Weather Quantities Using Graphical Models
The statistical creation of predictive distributions for weather quantities has enabled weather researchers to postprocess forecasts from numerical weather prediction models. Presently, this postprocessing is performed separately for each weather quantity of interest and therefore dependence between weather quantities is not captured in the resulting predictive distribution. In this project we investigate the construction of multivariate predictive distributions for weather quantities that incorporate these dependencies. In order to improve the predictive performance of these models we will consider the use of graphical models, both describing dependence between variables as well as the spatial and temporal dependence in weather patterns.
- Object and Action Recognition in Videos
This thesis deals with learning spatio-temporal patterns in videos to characterize the appearance, shape, and motion of objects from diverse categories that exhibit large within-class variability. Graphical models are then to be employed to model robust representations that facilitate the detection of objects and the classification of the actions that they perform.
- Cell tracking and lineage tree reconstruction in vertebrate embryos
A recent breakthrough in imaging permits the spatially and temporally resolved imaging of developing vertebrate embryos at the single cell level, up to around 20k cells. The first goal of this project is to establish a reliable tracking scheme within the framework of probabilistic graphical models that is amenable to terabyte-sized raw data sets. A second goal is the collection of statistics on lineage trees, both across multiple samples ascribed to a single individual, and across the trees inferred from multiple individuals. Taken together, this should enable new research on the genesis of organisms with a wealth of detail unavailable to date.
- Structural Pattern Recognition: Identifying Features and Physical Model Parameters
It has become clear and widely accepted that the structural pattern of chromosomes and the entire nucleus including all of the chromosomes of eukaryotes are highly dynamic. Hence in high resolution images of nuclei one finds a tremendously rich variety of local as well as overall structural patterns. These patterns relate to the exact point in time of the cell cycle, to the internal organization of a chromosome as well as to the type of cell. For example even a simple minded analysis in terms of a probabilistic model highlights structural differences between 3T3 and stem cells. To understand these difference one needs to develop methods that not only pick out the structural differences but relate them to physical models of the organization of chromosomes. These models are probabilistically hierarchical as there is structure within structure in a probabilistically sense. Hence graphical models that learn parameters unrelated to the underlying physical model are not of help. Thus we have to break now grounds in developing a method that on the one hand is able to extract features on multiple scales and on the other hand is consistent with a physical interpretation. This has become a very pressing issue as more and more data from a variety of sources (microscopy, expression analysis, HiC etc) is becoming available that needs to be integrated in a consistent manner to make progress in the understanding of the organization of life.
- Variational Models for Image Segmentation with Shape Priors
Prior knowledge about the shape of objects constitutes an important cue for image segmentation. Statistical models of shape range from elementary PCA-based models of closed contours to sophisticated shape manifolds that encode shapes in a more invariant way by abstracting from non-intrinsic shape variations. Complementing data-driven approaches to segmentation with shape priors typically result in highly nonconvex models that are difficult to handle from the optimization point-of-view.
The project will focus on recent progress concerning convex variational relaxations of the segmentation problem and on the inference and learning problem in connection with suitable shape priors represented by graphical models.
- Graphical Models for Point Processes
In the project graphical models for multivariate point processes shall be defined based on conditional intensity functions. The properties of such graphical models shall be investigated and statistical methods for the identification of the edges shall be developed. The methods shall in particular be used for the identification of functional neural connectivity from simultaneously recorded neural spike trains. The goal is to develop methods which are also able to discriminate between excitatory or inhibitory connections.
- Granger-Causality Graphs for Locally Stationary Processes
Granger causality graphs for multivariate stationary time series shall be extended to graphical models for nonstationary time series. By using the concept of local stationarity methods of statistical inference for such graphs shall be developed. A specific case of importance are graphical models where the processes are nonstationary but the graph itself stays time-invariant (an example being a neuronal system where certain neurons are connected). Here the classical procedures of identifying the parameters and the graph on moving segments are inappropriate since important information is not taken into account. Therefore it will be a special task of this PhD-project to develop methods for this situation.
- Inhomogenous Marked Point Processes for the Analysis of Texture Images
In this project, inhomogenous 2D-texture images are analyzed to detect their underlying 3D geometric structure. For these purposes, an image is regarded as a realization of an inhomogenous marked point process that needs to be developed based on a suitable dictionary of marks, an adequate scaling function, and a mapping algorithm incorporating both mark selection and transformation.