Jean Daniel Boissonnat
Frédéric Chazal
Mariette Yvinec
Goals
High dimensional geometric data are ubiquitous in science and engineering, and thus processing and analyzing them is a core task in these disciplines. Recently, a new geometric and topological approach to data analysis has emerged, extending the success story of geometric algorithms with guarantees to high-dimensions. This course is an introduction to the new field of Computational Geometry Learning providing mathematical and algorithmic foundations to geometric sampling and approximation.
This course is related to a new European project called CG-Learning (Computational Geometry Learning)
and involving research groups at INRIA Saclay, INRIA Sophia Antipolis, ETH Zurich, and in the universities of Iena, Dortmund, Berlin, Gronningen, Athens and Tel Aviv.
Language
The course will be given in english,
except if all participants speak french fluently.
Slides and course notes are in english.
Organisation
The course will include 10 sessions of 2h30 each.
Each lecture will include exercises.
- M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, Germany, 2nd edition, 2000.
- J-D. Boissonnat and M. Yvinec. Algorithmic Geometry. Cambridge University Press, UK, 1998. Translated by Hervé Brönnimann.
- K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, Englewood Cliffs, NJ, 1994.
- E. Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge, 2001.
- F. Chazal, D. Cohen-Steiner, A. Lieutier, A Sampling Theory for Compacts in Euclidean Space, Discrete Comput. Geom., 41:461-479, 2009.
- F. Chazal, D. Cohen-Steiner, Geometric Inference, submitted as a chapter in a book entitled "Tesselations in the Sciences", November 2007.
- A. Zomorodian, Topology for Computing, Cambridge Monographs on Applied and Computational Mathematics, cambridge University Press, 2005.
