Persistence modules, shape description, and completeness

Cagliari, Francesca ; Ferri, Massimo ; Gualandri, Luciano ; Landi, Claudia (2012) Persistence modules, shape description, and completeness. Springer LNCS, 7309 . pp. 148-156.
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Abstract

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the $H_0$-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor.

Abstract
Document type
Article
Creators
CreatorsAffiliationORCID
Cagliari, Francesca
Ferri, Massimo
Gualandri, Luciano
Landi, Claudia
Keywords
geometric homomorphism; rank invariant; $H_0$-tree
Subjects
DOI
Deposit date
28 Jul 2015 12:33
Last modified
28 Jul 2015 12:33
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