PHAT (Persistent Homology Algorithm Toolbox) ,
DOI : 10.1007/978-3-662-44199-2_24
Computing robustness and persistence for images, IEEE Transactions on Visualization and Computer Graphics, vol.16, issue.6, pp.1251-1260, 2010. ,
DOI : 10.1109/tvcg.2010.139
URL : http://www.mpi-sb.mpg.de/%7Emkerber/bek-crpi-2010.pdf
Persistent homology under non-uniform error, Mathematical Foundations of Computer Science, vol.6281, pp.12-23, 2010. ,
DOI : 10.1007/978-3-642-15155-2_2
URL : http://www.mpi-sb.mpg.de/%7Emkerber/BEKP_MFCS_10.pdf
A persistence landscapes toolbox for topological statistics, Journal of Symbolic Computations ,
DOI : 10.1016/j.jsc.2016.03.009
URL : https://hal.archives-ouvertes.fr/hal-01258875
The theory of multidimensional persistence, Discrete & Computational Geometry, vol.42, issue.1, pp.71-93, 2009. ,
DOI : 10.1145/1247069.1247105
URL : http://www.cs.dartmouth.edu/~afra/papers/socg07/multid.ps.gz
Hausdorff stability of persistence spaces, Foundations of Computational Mathematics, vol.16, issue.2, pp.343-367, 2016. ,
Betti numbers in multidimensional persistent homology are stable functions, Mathematical Methods in the Applied Sciences, vol.36, issue.12, pp.1543-1557, 2013. ,
Proximity of persistence modules and their diagrams, Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry, ACM SCG '09, pp.237-246, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00292566
The Structure and Stability of Persistence Modules, SpringerBriefs in Mathematics, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01107617
An optimal convex hull algorithm in any fixed dimension, Discrete & Computational Geometry, vol.10, issue.4, pp.377-409, 1993. ,
A randomized subdivision algorithm for determining the topology of nodal sets, SIAM Journal on Scientific Computing, vol.35, issue.5, pp.1034-1054, 2013. ,
Stability of persistence diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007. ,
Verified homology computations for nodal domains, SIAM Journal on Multiscale Modeling & Simulation, vol.7, issue.4, pp.1695-1726, 2009. ,
, Topology in dynamics, differential equations, and data, vol.334, pp.1-3, 2016.
, GUDHI: User and Reference Manual
Coreduction Homology Algorithm for Regular CW-Complexes, Discrete & Computational Geometry, vol.46, issue.2, pp.361-388, 2011. ,
Topological microstructure analysis using persistence landscapes, Physica D, vol.334, issue.1, pp.60-81, 2016. ,
, , 2010.
Topological persistence and simplification, Discrete & Computational Geometry, vol.29, issue.4, pp.511-533, 2002. ,
, Affine arithmetic: Concepts and applications, vol.37, pp.147-158, 2004.
A generalized interval arithmetic, Interval Mathematics, volume 29 of the series Lecture Notes in Computer Science, pp.7-18, 2005. ,
, Rigorous computation of persistent homology, accepted to Mathematics of Computation, 2016.
A Basic Course in Algebraic Topology, 1991. ,
Morse theory for filtrations and efficient computation of persistent homology, Discrete & Computational Geometry, vol.50, issue.2, pp.330-353, 2013. ,
Introduction to Interval Analysis, 2009. ,
,
, Coreduction homology algorithm for inclusions and persistent homology, vol.60, pp.2812-2833, 2010.
, Perseus, the Persistent Homology Software
, Interval Methods for Systems of Equations, 1990.
Topological analysis of the diblock copolymer equation, Mathematical Challenges in a New Phase of Materials Science, pp.27-51, 2016. ,
Homology Theory. An Introduction to Algebraic Topology, 1994. ,