Geometrical and Topological Data Analysis

Slides

• Gabriel Peyré (CNRS and ENS): Mesh Processing Meets Graph Theory.
• Pierre Alliez (INRIA): Digital Geometry Processing.
• Julien Tierny (CNRS and Paris 6): Topological Data Analysis for Scientific Vizualization.

Computational resources

• VTK, for vizualization.
• Paraview, for vizualization.
• For low dimensional topological data analysis: TTK (available in April 2017).
• For topological inference in high dimension: Gudhi.
• The numerical Tours of Signal Processing (in Matlab and Python) contains a section dedicated to mesh processing, including denoising, spectral analysis, parameterization, deformation.
• CGAL library

Bibliography

Here is a (biased) bibliography related to the lectures.

Related to vizualization:

• The Visualization Handbook, Johnson and Hansen, 2004.
• The Visualization ToolKit, Schroeder, Martin, Lorensen, 2006.
• Webpage of a course at ENSTA by Julien Tierny.
• A tutorial by Julien Tierny on paraview.
• A first tutorial by Julien Tierny on C++/VTK.
• A second one.

Related to topological data analysis:

• The definitive reference: Computational Topology: An Introduction, Edelsbrunner and Harer, AMS, 2010.
• Course notes by Julien Tirerny
• Course notes by Frédéric Chazal, in particular chap 11 for material related to statistical inference and machine learning.

Related to geometry processing:

• Polygon Mesh Processing, Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy.
• A Survey of Surface Reconstruction from Point Clouds, Matthew Berger, Andrea Tagliasacchi, Lee Seversky, Pierre Alliez, Gael Guennebaud, Joshua Levine, Andrei Sharf, Claudio Silva.