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Topological Data Analysis and Visualization: A Tutorial
Beteiligte : Julien Tierny (Pequan)Scientific visualization aims at helping users (i) represent, (ii) explore, and (iii) analyze acquired or simulated geometrical data, for interpretation, validation or communication purposes. Among the existing techniques, algorithms inspired by Morse theory have demonstrated their utility in this context for the efficient and robust extraction of geometrical features, at multiple scales of importance.
In this talk, I will give a brief tutorial on the topological methods used in scientific visualization for the analysis of scalar data. I will present algorithms with practical efficiency for the computation of topological abstractions (Reeb graphs, Morse-Smale complexes, persistence diagrams, etc.) in low dimensions (typically 2 or 3). I will also illustrate these notions with concrete use cases in astrophysics, fluid dynamics, molecular chemistry or combustion.
This seminar will be followed by a second tutorial, on May 4th, related to the design and usage of the open-source C++ library "the Topology ToolKit" (https://topology-tool-kit.github.io/), which implements most of the algorithms discussed in the first talk.
Marc.Mezzarobba (at) nulllip6.fr