Research

My research interests are in developing efficient and mathematical consistent
algorithms that solve Computer Vision problems. In particular I am interested
in problems that can be formulated as an energy minimization problem. In the
past I worked on shape related problems and on model estimation problems.
Depending on the problem, I worked either on discrete or continuous
approaches which involved but were not restricted to **Differential Geometry**,
**Partial Differential Equations**, **Convex and Non-Convex Optimization**
as well as **Planar Graphs**, **Integer Linear Programming** and
**Hierarchical Model Estimation**.

Recent Projects

## Image Segmentation

The goal of image segmentation is to seperate the image into multiple
regions. In our recent work using superlabels, we showed that even binary
segmentation can be stated as a multi-label problem with a more accurate
result than the classical Boykov-Jolly approach.

## 3D Shape Matching

The goal of shape matching is to find a correspondence map between two
different shapes. For 3D shapes, there exists no polynomeous runtime
methods that solve this problem globally. In our recent work, we showed
that by solving an ILP (Integer Linear Program) instance, the 3D shape
matching approach can be formulated in a geometrical consistent manner.

## 2D Shape Matching

In the case of planar shapes, the matching can be computed quite
efficiently, e.g., by different almost quadratic runtime approaches. We
presented methods that can do this by either finding multiple shortest
paths in a planar grid or by computing a minimal graph cut within a planar
graph.

## Shape Morphing

The set of all planar shapes can be described as a manifold in an infinite
dimensional vector space. By calculating the shortest distance between two
shapes (points on the manifold), we receive a transformation from one shape
into the other -- a so called morphing. We showed in our work that a
path-shortening approach can be much faster the previously used shooting
method.