# PhD Courses - Visualization

# Advanced Scientific Visualization - Mai 2016

# Topological Methods in Visualization - Mai 2017

**Summary:** With the increasing complexity of data, efficient methods for filtering and abstraction of the data become more and more important. Feature based methods, which try to extract interesting structures or patterns form the data, are one way to approach this challenge. Topological data analysis provides a successful concept for this purpose. The use of topological methods for visualization has lead to many very powerful techniques for feature extraction. In this lecture I will give an introduction to basic topological methods for scalar and vector fields. We will discus the use of these methods for some examples in the field of fluid mechanics.

**Aim:** Upon completion of the course the students should have a general understanding of the concept of topological methods for data analysis.

**Organization: **

The course is composed of 6 lectures followed by student presentations and projects.

**Course contents:**

- Feature based visualization
- Topology as a mathematical discipline
- Topology as a concept for data analysis
- Scalar field topology: Contour trees, Morse Smale complex, Forman's discrete Morse theory, Persistence based simplification, Applications
- Vector field topology
- Outlook: Tensor field topology

**Course literature: **

- Geometry and Topology for Mesh Generation, Herbert Edelsbrunner, 2001
- Computational Topology. An Introduction, Herbert Edelsbrunner, 2010
- Algebraic Topology, Allen Hatcher, 2001
- Original Papers from Transactions on Visualization and Computer Graphics, Computer Graphics Forum