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Computational Topology (seminar)



In this seminar we want to discuss relatively new research papers that use methods from algebraic topology to analyze data. A good introduction into the field can be found in the following books:

  • Afra Zomorodian. Topology for Computing. Cambridge University Press
  • Dmitry Kozlov. Combinatorial Algebraic Topology. Springer

The following papers could be presented in the seminar:

  1. V. de Silva. A weak characterisation of the Delaunay triangulation. Geometriae Dedicata, 135(1)
  2. V. de Silva, G. Carlsson. Topological estimation using witness complexes. Symposium on Point-Based Graphics
  3. G. Carlsson, T. Ishkhanov, V. de Silva, A. Zomorodian. On the local behavior of spaces of natural images. International Journal of Computer Vision, 76(1)
  4. G. Carlsson, V. de Silva. Topological approximation by small simplicial complexes. preprint
  5. G. Carlsson, A. Collins, L. Guibas, A. Zomorodian. Persistence Barcodes for Shapes. International Journal of Shape Modeling, 2005

The first four papers are available on Vin de Silva's homepage, and the last paper is available from Afra Zomorodian's homepage.

Here is an example from our own research, namely the scale axis transform that we use for topological and geometric multi-scale analysis of shapes. Increasing the parameter s simplifies the geometry while key topological features of the shape are kept.

ScaleAxis2

 

The seminar is organized by Martin Hünniger and Joachim Giesen. The seminar requires you to:

  • Present a paper or book chapter.
  • Provide a short written summary of the key ideas of the presented paper.
  • Actively participate in the seminar.

The first meeting where we discuss how to organize the seminar will take place Thursday 22. October at 8.15am in SR 125 CZ. See also CAJ.