# Bachelor and Master Theses

We permanently offer proposals for bachelor and master thesis projects in all areas across our research activities (see our research areas page) and related subjects which cover most topics in Virtual Reality and Scientific Visualization. The thesis topics are usually specified in cooperation with one of our research assistants and/or Prof. Kuhlen taking into account the student's individual interests and his/her previous knowledge as well as the current research agenda of the Virtual Reality group (e.g. in terms of ongoing academic or industrial cooperations). So if you are interested in a thesis project in Virtual Reality, please contact us. In order to guarantee a successful completion of the thesis, we usually expect our student to have

- taken the "Basic Techniques in Computer Graphics" lecture if you are a bachelor student
- taken the “Virtual Reality” lecture if you are a master student
- a good working knowledge of C++
- or an equivalent qualification.

## Bachelor/Master Thesis: Immersive Node Link Visualization of Invertible Neural Networks

Neural networks have the ability to approximate arbitrary functions. For example, neural networks can model manufacturing processes, i.e., given the machine parameters, a neural network can predict the properties of the resulting work piece. In practice, however, we are more interested in the inverse problem, i.e., given the desired work piece properties, generate the optimal machine parameters. Invertible neural networks (INNs) have shown to be well suited to address this challenge. However, like almost all kinds of neural networks, they are an opaque model. This means that humans cannot easily interpret the inner workings of INNs. To gain insights into the underlying process and the reasons for the model’s decisions, an immersive visualization should be developed in this thesis. The visualization should make use of the ANNtoNIA framework (developed at VCI), which is based on Python and Unreal Engine 4.

Requirements are a basic understanding of Machine Learning and Neural Networks as well as good Python programming skills. Understanding of C++ and Unreal Engine 4 is a bonus but not necessary.

Contact:

Martin Bellgardt, M. Sc.

## Master Thesis: The multi-device data- and task-parallelism library

There are various solutions for shared and distributed parallelism on CPUs and GPUs today: OpenMP and Intel Threading Building Blocks (TBB) for shared parallelism on the CPU, OpenCL and NVIDIA CUDA for shared parallelism on the GPU, MPI for distributed parallelism on both the CPU and the GPU. The majority of algorithms in scientific data analysis and visualization may be divided into two groups: data-parallel and task-parallel. Data-parallel approaches divide the domain into smaller chunks which are distributed to the processes, whereas task-parallel approaches divide the problem into smaller chunks and distribute them instead. The core idea of this engineering-oriented work is to develop a library enabling development of data-parallel and task-parallel visualization algorithms without explicit knowledge of the device the algorithm will run on.

Contact:

Ali Can Demiralp, M. Sc.

## Master Thesis: Numerical relativity library

Numerical relativity is one of the branches of general relativity that uses numerical methods to analyze problems. The primary goal of numerical relativity is to study spacetimes whose exact form is not known. Within this context the geodesic equation generalizes the notion of a straight line to curved spacetime. The core idea of this work is to develop a library for solving the geodesic equation, which in turn enables 4-dimensional spacetime ray tracing. The implementation should at least provide the Schwarzschild and Kerr solutions to the Einstein Field Equations, providing visualizations of non-rotating and rotating uncharged black holes.

Contact:

Ali Can Demiralp, M. Sc.

## Master Thesis: Mean curvature flow for truncated spherical harmonics expansions

Curvature flows produce successively smoother approximations of a given piece of geometry, by reducing a fairing energy. Within this context, mean curvature flow is a curvature flow defined for hypersurfaces in a Riemannian manifold (e.g. smooth 3D surfaces in Euclidean space), which emphasizes regions of higher frequency and converges to a sphere. Truncated spherical harmonics expansions are commonly used to represent scientific data as well as arbitrary geometric shapes. The core idea of this work is to establish the mathematical concept of mean curvature flow within the spherical harmonics basis, which is empirically done through interpolation of the harmonic coefficients to the coefficient 0,0.

Contact:

Ali Can Demiralp, M. Sc.

## Master Thesis: Orientation distribution function topology

Topological data analysis methods have been applied extensively to scalar and vector fields for revealing features such as critical and saddle points. There is recent effort on generalizing these approaches to tensor fields, although limited to 2D. Orientation distribution functions, which are the spherical analogue to a tensor, are often represented using truncated spherical harmonics expansions and are commonly used in visualization of medical and chemistry datasets. The core idea of this work is to establish the mathematical framework for extraction of topological skeletons from an orientation distribution function field.

Contact:

Ali Can Demiralp, M. Sc.

## Master Thesis: Block connectivity matrices

Connectivity matrices are square matrices for describing structural and functional connections between distinct brain regions. Traditionally, connectivity matrices are computed for segmented brain data, describing the connectivity e.g. among Brodmann areas in order to provide context to the neuroscientist. The core idea in this work is to take an alternative approach, dividing the data into a regular grid and computing the connectivity between each block, in a hierarchical manner. The presentation of such data as a matrix is non-trivial, since the blocks are in 3D and the matrix is bound to 2D, hence it is necessary to (a) reorder the data using space filling curves so that the spatial relationship between the blocks are preserved (b) seek alternative visualization techniques to replace the matrix (e.g. volume rendering).

Contact:

Ali Can Demiralp, M. Sc.