Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Retrieval of trademark images by means of size functions
Graphical Models - Special issue on the vision, video and graphics conference 2005
Stability of Persistence Diagrams
Discrete & Computational Geometry
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Multi-scale Representation and Persistency for Shape Description
MDA '08 Proceedings of the 3rd international conference on Advances in Mass Data Analysis of Images and Signals in Medicine, Biotechnology, Chemistry and Food Industry
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Computing Multidimensional Persistence
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Lipschitz Functions Have L p -Stable Persistence
Foundations of Computational Mathematics
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The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a pseudo-distance d T that represents a possible solution to this problem. Indeed, d T is a pseudo-distance between multidimensional persistent homology groups with coefficients in an Abelian group, hence possibly having torsion. Our main theorem proves the stability of the new pseudo-distance with respect to the change of the filtering function, expressed both with respect to the max-norm and to the natural pseudo-distance between topological spaces endowed with 驴 n -valued filtering functions. Furthermore, we prove a result showing the relationship between d T and the matching distance in the 1-dimensional case, when the homology coefficients are taken in a field and hence the comparison can be made.