The Persistence Space in Multidimensional Persistent Homology

  • Andrea Cerri
  • Claudia Landi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. Furthermore, it is presented a method to visualize topological features of a shape via persistence spaces. Finally, it is shown that this method is resistant to perturbations of the input data.


Topological Feature Homology Class Lower Dimensional Space Persistent Homology Multidimensional Analogue 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrea Cerri
    • 1
    • 3
  • Claudia Landi
    • 2
    • 3
  1. 1.IMATI – CNRGenovaItalia
  2. 2.DISMIUniversità di Modena e Reggio EmiliaItalia
  3. 3.ARCESUniversità di BolognaItalia

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