Im folgenden finden Sie eine Übersicht über einige der angebotenen Themen. Nahezu alle Quellen sind auf englisch, sowie die Themenbeschreibung. Die Arbeit selber darf in deutsch gehalten werden, jedoch wird empfohlen den Vortrag in englischer Sprache zu halten. Selbiges gilt für die Ausarbeitung.
Spectral Mesh Processing
Category: shape processing, numerical methods
Brief description of the topic:
The fourier transformation (the spectra of a function) is a widely used method for analysing and comparision of functions. In context of meshes, there are simular methods use the eigenvalues and eigenvectors of the laplace operator and similar approaches. These methods are used in various applications.
Task:
Give an overview of the needed numerical methods and the applications. A good starting point is the given reference.
Contact: Daniel Brandes ([email protected])
Lattice Boltzmann – Cellular Automata for Fluid Simulations
Category: Physical Simulation, Numerics, Parallelization
Brief description of the topic:
Lattice Boltzmann is a rather new method for simulating fluids. Other than traditional methods, it works similar to an cellular automaton and thus is a natural candidate for parallelizing the simulation. This has become more and more important over the last decade as parallel processing in general has become more significant.
Task:
Describe the Lattice Boltzmann method starting with the idea to the actual time and space discretization. Find recent work that has been done in the field of Lattice Boltzmann Fluid simulations and try to emphasize the advantages and disadvanteges of this method.
Contact: Maximilian Klein ([email protected])
Multiscale Visualization for biological data
Category: Multiscale Visualization, Medical Visualization
Brief Description of the topic:
Processes in the human body occur at different scales (from metres to nanometres, from microseconds to decades). Thus, there is a need for visualisation techniques that can support transition from one scale to another (for example, between organs, tissues and cells) in unified way.
Multiscale spatial visualisations have previously been developed in other areas, such as cartography, GIS and astrophysics. Despite several calls for multiscale visualization in the biomedical field, and the exponential increase in the size and complexity of their datasets, in recent years there have been several projects related to the multiscale spatial visualization in the field of biomedicine.
Task:
Describe how multiscale spatial techniques are used in the field of medical data visualization in recent projects, explaining the requirements of each project and how the use of these techniques satisfied that need.
Some references:
[1] O'Donoghue, et al.: Visualizing biological data—now and in the future. Nature methods 7, 2010.
[2] Fuchs, Hauser: Visualization of Multi-Variate Scientific Data. Computer Graphics Forum. Vol. 28. No. 6. Blackwell Publishing Ltd, 2009.
[3] Insley, Grinberg, Papka: Visualizing multiscale, multiphysics simulation data: Brain blood flow. IEEE Symposium on Large Data Analysis and Visualization (LDAV), 2011.
Contact: Ricardo Millan (rmillan(at)welfenlab.de)
Surface smoothing
Category: shape processing, numerical methods
Brief description of the topic:
A common task in shape processing is smoothing of irregular or noisy data. Such data can arise as a result of measurement from laser scanners or other devices. Common approaches include discretizations of geometric flows such as the mean curvature flow or the Willmore flow.
Task: Investigate the literature to gain an overview and describe a current approach dealing with this problem.
Some references:
[1]Taubin: A Signal Processing Approach to Fair Surface Design. SIGGRAPH 1995
[2]Bobenko, Schröder: Discrete Willmore Flow. SGP 2005
[3]Balzani,Rumpf: A nested variational time discretization for parametric Willmore flow, Interfaces and Free Boundaries, 2012
[4]Crane, Pinkall, Schröder: Robust Fairing via Conformal Curvature Flow, SIGGRAPH 2013
Contact: Alexander Vais (vais(at)welfenlab.de)
Parallelization of asynchrounous variational integrators
Category: Structural mechanics, Finite Element Methods
Brief description of the topic:
Structural mechanics are almost exclusively simulated using Finite Element Methods (FEM). These typically involve an implicit integration scheme - leading to the need of solving large systems of linear equations - or the more straightforward approach of an explicit integration scheme. One of the fundamental drawbacks of the latter method is the need for relatively small timesteps in order to achieve a stable simulation.
A relatively new class of integrators - the so called Asynchrounous Variational Integrators (AVIs) - tries to circumvent this problem by allowing for different timesteps on individual elements. However, the underlying datastructure is difficult to parallelize in order to benefit from modern computer architectures.
Task:
Briefly describe the AVI approach in comparison with traditional explicit integration schemes.
Describe (with focus on the underlying data structures) how the original AVI approach by Lew et al. has been modified to allow for parallel computation.
Reference:
[1] Lew et al.: Parallel asynchrounous variatonal integrators, Int. J. Numer. Meth. Engng 2007
Contact: Andreas Tarnowsky (tarnowsky(at)welfenlab.de)
Visualization of fiber orientation distributions in 3D models of anatomical skeletal muscles
Category: Medical visualization, Musculoskeletal modeling
Brief Description of the topic:
Computer models of the musculoskeletal system are commonly used to analyze the mechanisms of musculoskeletal disorders and to simulate surgical treatments. In this context, models that represent the 3D arrangement of muscle fibers and allow concrete specifications (variations of fiber lengths and moment arms) are needed in order to represent closely in vivo muscle behavior. There are different methods to specify the complex fiber orientations, and therefore, different ways of visualize them.
Task:
Give an overview of the current methods for visualizing the arrangement of muscle fibers comparing their respective visualization of the fiber orientation distributions.
References:
[1] Blemker, S.S. et al.: Image-based musculoskeletal modeling: Applications, advances, and future opportunities. Journal of Magnetic Resonance Imaging. 25, 2, 441–451 (2007).
[2] Blemker, S.S., Delp, S.L.: Three-Dimensional Representation of Complex Muscle Architectures and Geometries. Ann Biomed Eng. 33, 5, 661–673 (2005).
[3] Lu, Y.T. et al.: Modelling skeletal muscle fibre orientation arrangement. Computer Methods in Biomechanics and Biomedical Engineering. 14, 12, 1079–1088 (2011).
Contact: Ricardo Millan (rmillan(at)welfenlab.de)
