The Reeb graph is a popular tool in the field of computational topology for shape analysis. The Reeb graph is usually thought of as a transform from shapes, viewed as spaces endowed with functions, to graphs. It finds its roots in the classical Morse theory, where the Reeb graph transform is granted to produce a graph, but it finds its applications mostly in Computer Graphics. Therefore it is usually applied on objects that are not smooth but polyhedral. While the definition of the Reeb graph perfectly makes sense also in the polyhedral case, it is not straightforward to see that the output of the transform in this case is a graph. This paper is devoted to provide a formal guarantee of this fact.

Reeb Graphs of Piecewise Linear Functions / Di Fabio, Barbara; Landi, Claudia. - 10310:(2017), pp. 23-35. (Intervento presentato al convegno International Workshop on Graph-Based Representations in Pattern Recognition tenutosi a Anacapri (NA) nel 16-18 Maggio 2017) [10.1007/978-3-319-58961-9_3].

Reeb Graphs of Piecewise Linear Functions

DI FABIO, Barbara;LANDI, Claudia
2017

Abstract

The Reeb graph is a popular tool in the field of computational topology for shape analysis. The Reeb graph is usually thought of as a transform from shapes, viewed as spaces endowed with functions, to graphs. It finds its roots in the classical Morse theory, where the Reeb graph transform is granted to produce a graph, but it finds its applications mostly in Computer Graphics. Therefore it is usually applied on objects that are not smooth but polyhedral. While the definition of the Reeb graph perfectly makes sense also in the polyhedral case, it is not straightforward to see that the output of the transform in this case is a graph. This paper is devoted to provide a formal guarantee of this fact.
2017
International Workshop on Graph-Based Representations in Pattern Recognition
Anacapri (NA)
16-18 Maggio 2017
10310
23
35
Di Fabio, Barbara; Landi, Claudia
Reeb Graphs of Piecewise Linear Functions / Di Fabio, Barbara; Landi, Claudia. - 10310:(2017), pp. 23-35. (Intervento presentato al convegno International Workshop on Graph-Based Representations in Pattern Recognition tenutosi a Anacapri (NA) nel 16-18 Maggio 2017) [10.1007/978-3-319-58961-9_3].
File in questo prodotto:
File Dimensione Formato  
GbR2017-ReebGraphsPL.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 273.74 kB
Formato Adobe PDF
273.74 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1135448
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact