Interleaved Filtrations: Theory and Applications in Point Cloud Data Analysis

The aim of the talk at GSI’2013 is to introduce the audience to the concept of interleaving between filtrations, coming from applied topology, and to emphasize its influence on emerging trends in point cloud data analysis.

[1]  Leonidas J. Guibas,et al.  Gromov‐Hausdorff Stable Signatures for Shapes using Persistence , 2009, Comput. Graph. Forum.

[2]  Leonidas J. Guibas,et al.  Persistence-based clustering in riemannian manifolds , 2011, SoCG '11.

[3]  Tamal K. Dey,et al.  Manifold reconstruction from point samples , 2005, SODA '05.

[4]  Claudio Gutierrez,et al.  Survey of graph database models , 2008, CSUR.

[5]  Steve Oudot,et al.  Towards persistence-based reconstruction in euclidean spaces , 2007, SCG '08.

[6]  Steve Oudot,et al.  Persistence stability for geometric complexes , 2012, ArXiv.

[7]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[8]  Don Sheehy,et al.  Linear-Size Approximations to the Vietoris–Rips Filtration , 2012, Discrete & Computational Geometry.

[9]  Tamal K. Dey,et al.  Computing Topological Persistence for Simplicial Maps , 2012, SoCG.

[10]  R. Pollack,et al.  Surveys on discrete and computational geometry : twenty years later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah , 2008 .

[11]  Vin de Silva,et al.  A weak characterisation of the Delaunay triangulation , 2008 .

[12]  Gunnar E. Carlsson,et al.  Topological estimation using witness complexes , 2004, PBG.

[13]  Frédéric Chazal,et al.  Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$ , 2007, Discret. Comput. Geom..

[14]  Leonidas J. Guibas,et al.  Proximity of persistence modules and their diagrams , 2009, SCG '09.

[15]  Afra Zomorodian,et al.  Computing Persistent Homology , 2005, Discret. Comput. Geom..

[16]  Frédéric Chazal,et al.  A Sampling Theory for Compact Sets in Euclidean Space , 2009, Discret. Comput. Geom..

[17]  Daniela Giorgi,et al.  Describing shapes by geometrical-topological properties of real functions , 2008, CSUR.

[18]  Steve Oudot,et al.  Topological inference via meshing , 2010, SoCG '10.

[19]  Gunnar E. Carlsson,et al.  Zigzag Persistence , 2008, Found. Comput. Math..

[20]  Leonidas J. Guibas,et al.  Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes , 2007, SCG '07.

[21]  Leonidas J. Guibas,et al.  Analysis of scalar fields over point cloud data , 2009, SODA.

[22]  Steve Oudot,et al.  Zigzag zoology: rips zigzags for homology inference , 2013, SoCG '13.

[23]  David Cohen-Steiner,et al.  Stability of Persistence Diagrams , 2007, Discret. Comput. Geom..

[24]  Kim Steenstrup Pedersen,et al.  The Nonlinear Statistics of High-Contrast Patches in Natural Images , 2003, International Journal of Computer Vision.